Identifier
Mp00017: to 312-avoiding permutationPermutations
Mp00175: Permutations inverse Foata bijectionPermutations
Mp00114: Permutations connectivity setBinary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=> [.,[.,.]]=>[2,1]=>[2,1]=>0 [[.,.],.]=>[1,2]=>[1,2]=>1 [.,[.,[.,.]]]=>[3,2,1]=>[3,2,1]=>00 [.,[[.,.],.]]=>[2,3,1]=>[2,3,1]=>00 [[.,.],[.,.]]=>[1,3,2]=>[3,1,2]=>00 [[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>01 [[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>11 [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1]=>000 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>[3,4,2,1]=>000 [.,[[.,.],[.,.]]]=>[2,4,3,1]=>[4,2,3,1]=>000 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[3,2,4,1]=>000 [.,[[[.,.],.],.]]=>[2,3,4,1]=>[2,3,4,1]=>000 [[.,.],[.,[.,.]]]=>[1,4,3,2]=>[4,3,1,2]=>000 [[.,.],[[.,.],.]]=>[1,3,4,2]=>[3,4,1,2]=>000 [[.,[.,.]],[.,.]]=>[2,1,4,3]=>[2,4,1,3]=>000 [[[.,.],.],[.,.]]=>[1,2,4,3]=>[4,1,2,3]=>000 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>001 [[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,3,1,4]=>001 [[[.,.],[.,.]],.]=>[1,3,2,4]=>[3,1,2,4]=>001 [[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>011 [[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>111 [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[4,5,3,2,1]=>0000 [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5,3,4,2,1]=>0000 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[4,3,5,2,1]=>0000 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,4,5,2,1]=>0000 [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,4,2,3,1]=>0000 [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[4,5,2,3,1]=>0000 [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[3,5,2,4,1]=>0000 [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,2,3,4,1]=>0000 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[4,3,2,5,1]=>0000 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,4,2,5,1]=>0000 [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[4,2,3,5,1]=>0000 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,2,4,5,1]=>0000 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[2,3,4,5,1]=>0000 [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[5,4,3,1,2]=>0000 [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[4,5,3,1,2]=>0000 [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[5,3,4,1,2]=>0000 [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[4,3,5,1,2]=>0000 [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[3,4,5,1,2]=>0000 [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[5,2,4,1,3]=>0000 [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[2,4,5,1,3]=>0000 [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[5,4,1,2,3]=>0000 [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[4,5,1,2,3]=>0000 [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[3,2,5,1,4]=>0000 [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[2,3,5,1,4]=>0000 [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[3,5,1,2,4]=>0000 [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[2,5,1,3,4]=>0000 [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[5,1,2,3,4]=>0000 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>0001 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[3,4,2,1,5]=>0001 [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[4,2,3,1,5]=>0001 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,2,4,1,5]=>0001 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[2,3,4,1,5]=>0001 [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[4,3,1,2,5]=>0001 [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[3,4,1,2,5]=>0001 [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[2,4,1,3,5]=>0001 [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[4,1,2,3,5]=>0001 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>0011 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,3,1,4,5]=>0011 [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[3,1,2,4,5]=>0011 [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>0111 [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>1111 [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000 [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[5,6,4,3,2,1]=>00000 [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6,4,5,3,2,1]=>00000 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[5,4,6,3,2,1]=>00000 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[4,5,6,3,2,1]=>00000 [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>00000 [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[5,6,3,4,2,1]=>00000 [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[4,6,3,5,2,1]=>00000 [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,3,4,5,2,1]=>00000 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[5,4,3,6,2,1]=>00000 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[4,5,3,6,2,1]=>00000 [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[5,3,4,6,2,1]=>00000 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[4,3,5,6,2,1]=>00000 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[3,4,5,6,2,1]=>00000 [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,5,4,2,3,1]=>00000 [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[5,6,4,2,3,1]=>00000 [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,4,5,2,3,1]=>00000 [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[5,4,6,2,3,1]=>00000 [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[4,5,6,2,3,1]=>00000 [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,3,5,2,4,1]=>00000 [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[3,5,6,2,4,1]=>00000 [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,5,2,3,4,1]=>00000 [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[5,6,2,3,4,1]=>00000 [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[4,3,6,2,5,1]=>00000 [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[3,4,6,2,5,1]=>00000 [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[4,6,2,3,5,1]=>00000 [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[3,6,2,4,5,1]=>00000 [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>00000 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1]=>00000 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[4,5,3,2,6,1]=>00000 [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[5,3,4,2,6,1]=>00000 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[4,3,5,2,6,1]=>00000 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,4,5,2,6,1]=>00000 [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[5,4,2,3,6,1]=>00000 [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[4,5,2,3,6,1]=>00000 [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[3,5,2,4,6,1]=>00000 [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[5,2,3,4,6,1]=>00000 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1]=>00000 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[3,4,2,5,6,1]=>00000 [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[4,2,3,5,6,1]=>00000 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1]=>00000 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1]=>00000 [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>00000 [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[5,6,4,3,1,2]=>00000 [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[6,4,5,3,1,2]=>00000 [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[5,4,6,3,1,2]=>00000 [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[4,5,6,3,1,2]=>00000 [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[6,5,3,4,1,2]=>00000 [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[5,6,3,4,1,2]=>00000 [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[4,6,3,5,1,2]=>00000 [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[6,3,4,5,1,2]=>00000 [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[5,4,3,6,1,2]=>00000 [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[4,5,3,6,1,2]=>00000 [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[5,3,4,6,1,2]=>00000 [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[4,3,5,6,1,2]=>00000 [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[3,4,5,6,1,2]=>00000 [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[6,5,2,4,1,3]=>00000 [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[5,6,2,4,1,3]=>00000 [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[6,2,4,5,1,3]=>00000 [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[5,2,4,6,1,3]=>00000 [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[2,4,5,6,1,3]=>00000 [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>00000 [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[5,6,4,1,2,3]=>00000 [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[6,4,5,1,2,3]=>00000 [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[5,4,6,1,2,3]=>00000 [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[4,5,6,1,2,3]=>00000 [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[3,6,2,5,1,4]=>00000 [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[3,2,5,6,1,4]=>00000 [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[6,2,3,5,1,4]=>00000 [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[2,3,5,6,1,4]=>00000 [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[6,3,5,1,2,4]=>00000 [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[3,5,6,1,2,4]=>00000 [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[6,2,5,1,3,4]=>00000 [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[2,5,6,1,3,4]=>00000 [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>00000 [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[5,6,1,2,3,4]=>00000 [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[4,3,2,6,1,5]=>00000 [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[3,4,2,6,1,5]=>00000 [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[4,2,3,6,1,5]=>00000 [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[3,2,4,6,1,5]=>00000 [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[2,3,4,6,1,5]=>00000 [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[4,3,6,1,2,5]=>00000 [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[3,4,6,1,2,5]=>00000 [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[2,4,6,1,3,5]=>00000 [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[4,6,1,2,3,5]=>00000 [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[3,2,6,1,4,5]=>00000 [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[2,3,6,1,4,5]=>00000 [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[3,6,1,2,4,5]=>00000 [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[2,6,1,3,4,5]=>00000 [[[[[.,.],.],.],.],[.,.]]=>[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]=>00001 [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[4,5,3,2,1,6]=>00001 [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[5,3,4,2,1,6]=>00001 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[4,3,5,2,1,6]=>00001 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,4,5,2,1,6]=>00001 [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[5,4,2,3,1,6]=>00001 [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[4,5,2,3,1,6]=>00001 [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[3,5,2,4,1,6]=>00001 [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>00001 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[4,3,2,5,1,6]=>00001 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[3,4,2,5,1,6]=>00001 [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[4,2,3,5,1,6]=>00001 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[3,2,4,5,1,6]=>00001 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[2,3,4,5,1,6]=>00001 [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]=>00001 [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[4,5,3,1,2,6]=>00001 [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[5,3,4,1,2,6]=>00001 [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[4,3,5,1,2,6]=>00001 [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[3,4,5,1,2,6]=>00001 [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[5,2,4,1,3,6]=>00001 [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[2,4,5,1,3,6]=>00001 [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]=>00001 [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[4,5,1,2,3,6]=>00001 [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[3,2,5,1,4,6]=>00001 [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[2,3,5,1,4,6]=>00001 [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[3,5,1,2,4,6]=>00001 [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[2,5,1,3,4,6]=>00001 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[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[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]=>[8,7,5,6,4,3,2,1]=>0000000 [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>[8,5,6,7,4,3,2,1]=>0000000 [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[7,6,5,8,4,3,2,1]=>0000000 [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[6,7,5,8,4,3,2,1]=>0000000 [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[5,6,7,8,4,3,2,1]=>0000000 [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[7,6,5,4,8,3,2,1]=>0000000 [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[6,7,5,4,8,3,2,1]=>0000000 [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>[7,5,6,4,8,3,2,1]=>0000000 [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[6,5,7,4,8,3,2,1]=>0000000 [.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[5,6,7,4,8,3,2,1]=>0000000 [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[7,6,4,5,8,3,2,1]=>0000000 [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>[6,7,4,5,8,3,2,1]=>0000000 [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>[5,7,4,6,8,3,2,1]=>0000000 [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>[7,4,5,6,8,3,2,1]=>0000000 [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[6,5,4,7,8,3,2,1]=>0000000 [.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[5,6,4,7,8,3,2,1]=>0000000 [.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>[6,4,5,7,8,3,2,1]=>0000000 [.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[5,4,6,7,8,3,2,1]=>0000000 [.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[4,5,6,7,8,3,2,1]=>0000000 [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[8,7,5,6,3,4,2,1]=>0000000 [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[7,8,5,6,3,4,2,1]=>0000000 [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[3,6,5,8,7,4,2,1]=>[6,8,5,7,3,4,2,1]=>0000000 [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[3,5,6,8,7,4,2,1]=>[8,5,6,7,3,4,2,1]=>0000000 [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>[7,6,5,8,3,4,2,1]=>0000000 [.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>[6,7,5,8,3,4,2,1]=>0000000 [.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[5,6,7,8,3,4,2,1]=>0000000 [.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>[4,6,7,8,3,5,2,1]=>0000000 [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>[8,7,6,3,4,5,2,1]=>0000000 [.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[3,4,7,6,8,5,2,1]=>[7,6,8,3,4,5,2,1]=>0000000 [.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>[6,7,8,3,4,5,2,1]=>0000000 [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[5,4,3,8,7,6,2,1]=>[5,8,4,7,3,6,2,1]=>0000000 [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>[5,4,7,8,3,6,2,1]=>0000000 [.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[4,5,3,7,8,6,2,1]=>[4,5,7,8,3,6,2,1]=>0000000 [.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>[4,7,8,3,5,6,2,1]=>0000000 [.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>[4,5,6,8,3,7,2,1]=>0000000 [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[4,6,8,3,5,7,2,1]=>0000000 [.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>[4,5,8,3,6,7,2,1]=>0000000 [.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[4,3,5,6,8,7,2,1]=>[4,8,3,5,6,7,2,1]=>0000000 [.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[5,4,6,7,3,8,2,1]=>0000000 [.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[4,5,6,7,3,8,2,1]=>0000000 [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>[7,6,3,4,5,8,2,1]=>0000000 [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[5,4,3,7,6,8,2,1]=>[5,4,7,3,6,8,2,1]=>0000000 [.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>[4,5,7,3,6,8,2,1]=>0000000 [.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1]=>[4,7,3,5,6,8,2,1]=>0000000 [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[6,5,4,3,7,8,2,1]=>0000000 [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[2,6,5,8,7,4,3,1]=>[6,8,5,7,4,2,3,1]=>0000000 [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[2,5,6,8,7,4,3,1]=>[8,5,6,7,4,2,3,1]=>0000000 [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[2,7,6,5,8,4,3,1]=>[7,6,5,8,4,2,3,1]=>0000000 [.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[2,6,7,5,8,4,3,1]=>[6,7,5,8,4,2,3,1]=>0000000 [.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[5,6,7,8,4,2,3,1]=>0000000 [.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[2,4,6,7,8,5,3,1]=>[6,7,8,4,5,2,3,1]=>0000000 [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>[8,7,6,3,5,2,4,1]=>0000000 [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[3,2,7,6,5,8,4,1]=>[7,6,3,5,8,2,4,1]=>0000000 [.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>[3,5,6,7,8,2,4,1]=>0000000 [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[8,7,6,5,2,3,4,1]=>0000000 [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[2,3,6,8,7,5,4,1]=>[8,6,7,5,2,3,4,1]=>0000000 [.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[2,3,6,7,8,5,4,1]=>[6,7,8,5,2,3,4,1]=>0000000 [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[2,3,5,8,7,6,4,1]=>[8,7,5,6,2,3,4,1]=>0000000 [.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[2,3,7,6,5,8,4,1]=>[7,6,5,8,2,3,4,1]=>0000000 [.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[2,3,6,7,5,8,4,1]=>[6,7,5,8,2,3,4,1]=>0000000 [.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[5,6,7,8,2,3,4,1]=>0000000 [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[8,4,7,3,6,2,5,1]=>0000000 [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[4,3,2,7,8,6,5,1]=>[4,7,8,3,6,2,5,1]=>0000000 [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>[4,8,3,6,7,2,5,1]=>0000000 [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[8,7,6,2,3,4,5,1]=>0000000 [.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[2,3,4,7,8,6,5,1]=>[7,8,6,2,3,4,5,1]=>0000000 [.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[2,3,4,6,8,7,5,1]=>[8,6,7,2,3,4,5,1]=>0000000 [.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>[6,7,8,2,3,4,5,1]=>0000000 [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[4,5,3,2,8,7,6,1]=>[4,5,8,3,7,2,6,1]=>0000000 [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>[4,8,3,5,7,2,6,1]=>0000000 [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>[4,8,3,7,2,5,6,1]=>0000000 [.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[3,4,2,5,7,8,6,1]=>[3,4,7,8,2,5,6,1]=>0000000 [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>[6,5,4,3,8,2,7,1]=>0000000 [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>[6,4,5,3,8,2,7,1]=>0000000 [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>[5,4,6,3,8,2,7,1]=>0000000 [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[3,5,6,4,2,8,7,1]=>[5,6,3,4,8,2,7,1]=>0000000 [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[4,6,3,5,8,2,7,1]=>0000000 [.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[4,5,6,7,3,2,8,1]=>0000000 [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>[5,4,7,3,6,2,8,1]=>0000000 [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[6,5,4,3,7,2,8,1]=>0000000 [.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>[6,4,5,3,7,2,8,1]=>0000000 [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[5,4,6,3,7,2,8,1]=>0000000 [.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>[6,5,3,4,7,2,8,1]=>0000000 [.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[5,6,3,4,7,2,8,1]=>0000000 [.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[4,6,3,5,7,2,8,1]=>0000000 [.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[5,4,3,6,7,2,8,1]=>0000000 [.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>[5,4,6,7,2,3,8,1]=>0000000 [.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>[6,7,3,5,2,4,8,1]=>0000000 [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>[7,6,5,2,3,4,8,1]=>0000000 [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>[4,7,3,6,2,5,8,1]=>0000000 [.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[4,3,5,7,2,6,8,1]=>0000000 [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[6,5,4,3,2,7,8,1]=>0000000 [.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[5,4,6,3,2,7,8,1]=>0000000 [.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[5,4,3,6,2,7,8,1]=>0000000 [.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[3,4,5,6,2,7,8,1]=>0000000 [.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>[5,4,6,2,3,7,8,1]=>0000000 [.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>[6,5,2,3,4,7,8,1]=>0000000 [.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[5,4,3,2,6,7,8,1]=>0000000 [.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,8,1]=>0000000 [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[7,8,6,5,4,3,1,2]=>0000000 [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[7,6,5,8,4,3,1,2]=>0000000 [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[6,7,5,8,4,3,1,2]=>0000000 [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>[7,5,6,8,4,3,1,2]=>0000000 [[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[5,6,7,8,4,3,1,2]=>0000000 [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>[8,6,7,4,5,3,1,2]=>0000000 [[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,4,5,7,8,6,3,2]=>[7,8,4,5,6,3,1,2]=>0000000 [[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,6,5,7,4,8,3,2]=>[6,5,7,4,8,3,1,2]=>0000000 [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,4,7,6,5,8,3,2]=>[7,6,4,5,8,3,1,2]=>0000000 [[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,4,6,7,5,8,3,2]=>[6,7,4,5,8,3,1,2]=>0000000 [[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,4,5,6,7,8,3,2]=>[4,5,6,7,8,3,1,2]=>0000000 [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[7,8,5,6,3,4,1,2]=>0000000 [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,3,6,5,8,7,4,2]=>[6,8,5,7,3,4,1,2]=>0000000 [[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,3,6,7,5,8,4,2]=>[6,7,5,8,3,4,1,2]=>0000000 [[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,3,5,7,6,8,4,2]=>[7,5,6,8,3,4,1,2]=>0000000 [[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>[6,5,7,8,3,4,1,2]=>0000000 [[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[5,6,7,8,3,4,1,2]=>0000000 [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>[7,8,4,6,3,5,1,2]=>0000000 [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>[7,4,6,8,3,5,1,2]=>0000000 [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>[8,7,6,3,4,5,1,2]=>0000000 [[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,3,4,7,8,6,5,2]=>[7,8,6,3,4,5,1,2]=>0000000 [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>[5,8,4,7,3,6,1,2]=>0000000 [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,4,5,3,8,7,6,2]=>[8,4,5,7,3,6,1,2]=>0000000 [[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>[5,6,4,8,3,7,1,2]=>0000000 [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[4,6,8,3,5,7,1,2]=>0000000 [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>[5,4,8,3,6,7,1,2]=>0000000 [[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,4,5,3,6,8,7,2]=>[4,5,8,3,6,7,1,2]=>0000000 [[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,4,6,7,5,3,8,2]=>[6,7,4,5,3,8,1,2]=>0000000 [[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,5,4,7,6,3,8,2]=>[5,7,4,6,3,8,1,2]=>0000000 [[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,4,5,6,7,3,8,2]=>[4,5,6,7,3,8,1,2]=>0000000 [[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,4,3,6,7,5,8,2]=>[4,6,7,3,5,8,1,2]=>0000000 [[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,3,4,7,6,5,8,2]=>[7,6,3,4,5,8,1,2]=>0000000 [[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,5,4,3,7,6,8,2]=>[5,4,7,3,6,8,1,2]=>0000000 [[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,6,5,4,3,7,8,2]=>[6,5,4,3,7,8,1,2]=>0000000 [[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,3,5,6,4,7,8,2]=>[5,6,3,4,7,8,1,2]=>0000000 [[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,3,4,6,5,7,8,2]=>[6,3,4,5,7,8,1,2]=>0000000 [[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[5,4,3,6,7,8,1,2]=>0000000 [[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>[4,5,3,6,7,8,1,2]=>0000000 [[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,3,5,4,6,7,8,2]=>[5,3,4,6,7,8,1,2]=>0000000 [[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>[3,4,5,6,7,8,1,2]=>0000000 [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[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]=>[6,7,8,5,2,4,1,3]=>0000000 [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[7,8,5,6,2,4,1,3]=>0000000 [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[6,8,5,7,2,4,1,3]=>0000000 [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[7,6,5,8,2,4,1,3]=>0000000 [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[6,7,5,8,2,4,1,3]=>0000000 [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[2,1,5,7,6,8,4,3]=>[7,5,6,8,2,4,1,3]=>0000000 [[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[5,6,7,8,2,4,1,3]=>0000000 [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>[7,6,2,4,5,8,1,3]=>0000000 [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[6,7,8,5,4,1,2,3]=>0000000 [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,2,6,5,8,7,4,3]=>[6,8,5,7,4,1,2,3]=>0000000 [[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,2,5,6,8,7,4,3]=>[8,5,6,7,4,1,2,3]=>0000000 [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>[7,6,5,8,4,1,2,3]=>0000000 [[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,2,6,7,5,8,4,3]=>[6,7,5,8,4,1,2,3]=>0000000 [[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,2,6,5,7,8,4,3]=>[6,5,7,8,4,1,2,3]=>0000000 [[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[5,6,7,8,4,1,2,3]=>0000000 [[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>[8,6,7,4,5,1,2,3]=>0000000 [[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,2,4,6,7,5,8,3]=>[6,7,4,5,8,1,2,3]=>0000000 [[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>[6,5,4,7,8,1,2,3]=>0000000 [[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[5,4,6,7,8,1,2,3]=>0000000 [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>[7,8,3,6,2,5,1,4]=>0000000 [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[8,3,7,2,5,6,1,4]=>0000000 [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[3,8,2,5,6,7,1,4]=>0000000 [[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[3,2,5,6,7,8,1,4]=>0000000 [[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[7,6,8,2,3,5,1,4]=>0000000 [[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[2,3,1,5,6,8,7,4]=>[8,2,3,5,6,7,1,4]=>0000000 [[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[2,3,5,6,7,8,1,4]=>0000000 [[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>[7,8,3,5,6,1,2,4]=>0000000 [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>[7,8,6,2,5,1,3,4]=>0000000 [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>[8,6,7,2,5,1,3,4]=>0000000 [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[2,1,3,5,8,7,6,4]=>[8,7,2,5,6,1,3,4]=>0000000 [[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[2,1,3,5,7,8,6,4]=>[7,8,2,5,6,1,3,4]=>0000000 [[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[2,1,3,6,5,7,8,4]=>[6,2,5,7,8,1,3,4]=>0000000 [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[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]=>[7,8,6,5,1,2,3,4]=>0000000 [[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>[8,6,7,5,1,2,3,4]=>0000000 [[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[7,6,8,5,1,2,3,4]=>0000000 [[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>[6,7,8,5,1,2,3,4]=>0000000 [[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[8,7,5,6,1,2,3,4]=>0000000 [[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[7,8,5,6,1,2,3,4]=>0000000 [[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[6,8,5,7,1,2,3,4]=>0000000 [[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[8,5,6,7,1,2,3,4]=>0000000 [[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[7,6,5,8,1,2,3,4]=>0000000 [[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[6,7,5,8,1,2,3,4]=>0000000 [[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>[7,5,6,8,1,2,3,4]=>0000000 [[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[6,5,7,8,1,2,3,4]=>0000000 [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[5,6,7,8,1,2,3,4]=>0000000 [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[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]=>[4,3,7,8,2,6,1,5]=>0000000 [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[4,3,8,2,6,7,1,5]=>0000000 [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[4,3,7,2,6,8,1,5]=>0000000 [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[4,3,2,6,7,8,1,5]=>0000000 [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[8,3,4,7,2,6,1,5]=>0000000 [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[3,4,7,8,2,6,1,5]=>0000000 [[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[3,4,7,2,6,8,1,5]=>0000000 [[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[3,4,2,6,7,8,1,5]=>0000000 [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[8,4,7,2,3,6,1,5]=>0000000 [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[4,8,2,3,6,7,1,5]=>0000000 [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[8,3,7,2,4,6,1,5]=>0000000 [[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[3,7,8,2,4,6,1,5]=>0000000 [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[8,7,2,3,4,6,1,5]=>0000000 [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[2,3,4,6,7,8,1,5]=>0000000 [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[8,4,7,3,6,1,2,5]=>0000000 [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[4,7,3,6,8,1,2,5]=>0000000 [[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[4,3,6,7,8,1,2,5]=>0000000 [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[8,7,3,4,6,1,2,5]=>0000000 [[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>[7,8,3,4,6,1,2,5]=>0000000 [[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[3,4,6,7,8,1,2,5]=>0000000 [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[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]=>[7,8,2,4,6,1,3,5]=>0000000 [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[8,2,4,6,7,1,3,5]=>0000000 [[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[2,4,6,7,8,1,3,5]=>0000000 [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[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]=>[7,8,4,6,1,2,3,5]=>0000000 [[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>[8,4,6,7,1,2,3,5]=>0000000 [[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>[4,6,7,8,1,2,3,5]=>0000000 [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[8,3,7,2,6,1,4,5]=>0000000 [[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[3,2,6,7,8,1,4,5]=>0000000 [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[8,7,2,3,6,1,4,5]=>0000000 [[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>[7,8,2,3,6,1,4,5]=>0000000 [[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[2,3,6,7,8,1,4,5]=>0000000 [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[8,7,3,6,1,2,4,5]=>0000000 [[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>[3,6,7,8,1,2,4,5]=>0000000 [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[8,7,2,6,1,3,4,5]=>0000000 [[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[2,6,7,8,1,3,4,5]=>0000000 [[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[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]=>[7,8,6,1,2,3,4,5]=>0000000 [[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>[8,6,7,1,2,3,4,5]=>0000000 [[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[7,6,8,1,2,3,4,5]=>0000000 [[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[6,7,8,1,2,3,4,5]=>0000000 [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[5,4,3,2,7,8,1,6]=>0000000 [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>[4,5,3,8,2,7,1,6]=>0000000 [[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>[3,4,5,8,2,7,1,6]=>0000000 [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[4,3,8,2,5,7,1,6]=>0000000 [[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[4,3,2,5,1,7,8,6]=>[4,3,2,5,7,8,1,6]=>0000000 [[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[3,2,4,5,1,7,8,6]=>[3,2,4,5,7,8,1,6]=>0000000 [[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[8,2,3,4,5,7,1,6]=>0000000 [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,5,4,3,2,7,8,6]=>[5,4,3,7,8,1,2,6]=>0000000 [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[2,1,5,4,3,7,8,6]=>[5,2,4,7,8,1,3,6]=>0000000 [[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>[5,4,7,8,1,2,3,6]=>0000000 [[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[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]=>[5,7,8,1,2,3,4,6]=>0000000 [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[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]=>[4,3,2,7,8,1,5,6]=>0000000 [[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[3,2,4,7,8,1,5,6]=>0000000 [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[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]=>[4,3,7,8,1,2,5,6]=>0000000 [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[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]=>[3,2,7,8,1,4,5,6]=>0000000 [[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[2,3,1,4,5,8,7,6]=>[8,2,3,7,1,4,5,6]=>0000000 [[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[7,8,1,2,3,4,5,6]=>0000000 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[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]=>[5,6,4,3,2,8,1,7]=>0000000 [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>[6,4,5,3,2,8,1,7]=>0000000 [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[4,5,6,3,2,8,1,7]=>0000000 [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[6,5,3,4,2,8,1,7]=>0000000 [[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[5,6,3,4,2,8,1,7]=>0000000 [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>[4,6,3,5,2,8,1,7]=>0000000 [[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[4,5,3,6,2,8,1,7]=>0000000 [[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>[3,4,5,6,2,8,1,7]=>0000000 [[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[2,5,6,4,3,1,8,7]=>[5,6,4,2,3,8,1,7]=>0000000 [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>[6,4,5,2,3,8,1,7]=>0000000 [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[6,5,2,3,4,8,1,7]=>0000000 [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>[5,4,3,2,6,8,1,7]=>0000000 [[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,3,4,5,6,2,8,7]=>[3,4,5,6,8,1,2,7]=>0000000 [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[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]=>[5,6,2,4,8,1,3,7]=>0000000 [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[6,2,4,5,8,1,3,7]=>0000000 [[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,2,4,5,6,3,8,7]=>[4,5,6,8,1,2,3,7]=>0000000 [[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[3,2,1,5,6,4,8,7]=>[3,2,5,6,8,1,4,7]=>0000000 [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>[6,2,3,5,8,1,4,7]=>0000000 [[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[2,3,1,5,6,4,8,7]=>[2,3,5,6,8,1,4,7]=>0000000 [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[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]=>[6,5,8,1,2,3,4,7]=>0000000 [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[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]=>[3,4,2,6,8,1,5,7]=>0000000 [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[4,2,3,6,8,1,5,7]=>0000000 [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[3,2,4,6,8,1,5,7]=>0000000 [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[2,4,6,8,1,3,5,7]=>0000000 [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]=>[3,2,6,8,1,4,5,7]=>0000000 [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[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]=>[5,4,2,3,8,1,6,7]=>0000000 [[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>[3,5,2,4,8,1,6,7]=>0000000 [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[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]=>[5,2,4,8,1,3,6,7]=>0000000 [[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>[5,4,8,1,2,3,6,7]=>0000000 [[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,2,4,5,3,6,8,7]=>[4,5,8,1,2,3,6,7]=>0000000 [[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[3,2,1,5,4,6,8,7]=>[3,2,5,8,1,4,6,7]=>0000000 [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[4,3,2,8,1,5,6,7]=>0000000 [[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[3,2,4,8,1,5,6,7]=>0000000 [[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[2,3,4,8,1,5,6,7]=>0000000 [[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>[4,8,1,2,3,5,6,7]=>0000000 [[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]=>[3,2,8,1,4,5,6,7]=>0000000 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[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]=>[6,7,5,4,3,2,1,8]=>0000001 [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[7,5,6,4,3,2,1,8]=>0000001 [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[6,5,7,4,3,2,1,8]=>0000001 [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[5,6,7,4,3,2,1,8]=>0000001 [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[7,6,4,5,3,2,1,8]=>0000001 [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[6,5,4,7,3,2,1,8]=>0000001 [[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[5,6,4,7,3,2,1,8]=>0000001 [[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[4,5,6,7,3,2,1,8]=>0000001 [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>[7,5,6,3,4,2,1,8]=>0000001 [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[7,6,3,4,5,2,1,8]=>0000001 [[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>[4,7,3,5,6,2,1,8]=>0000001 [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[6,5,4,3,7,2,1,8]=>0000001 [[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[5,4,6,3,7,2,1,8]=>0000001 [[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[5,4,3,6,7,2,1,8]=>0000001 [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[2,4,7,6,5,3,1,8]=>[7,6,4,5,2,3,1,8]=>0000001 [[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[6,7,4,5,2,3,1,8]=>0000001 [[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[2,5,6,4,7,3,1,8]=>[5,6,4,7,2,3,1,8]=>0000001 [[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>[6,7,3,5,2,4,1,8]=>0000001 [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>[7,6,5,2,3,4,1,8]=>0000001 [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[4,3,2,7,6,5,1,8]=>[4,7,3,6,2,5,1,8]=>0000001 [[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>[7,6,2,3,4,5,1,8]=>0000001 [[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[4,5,3,7,2,6,1,8]=>0000001 [[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>[5,3,4,7,2,6,1,8]=>0000001 [[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[3,5,7,2,4,6,1,8]=>0000001 [[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[5,4,6,3,2,7,1,8]=>0000001 [[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[4,3,6,5,2,7,1,8]=>[4,6,3,5,2,7,1,8]=>0000001 [[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>[6,3,4,5,2,7,1,8]=>0000001 [[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[5,4,3,6,2,7,1,8]=>0000001 [[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[4,5,3,6,2,7,1,8]=>0000001 [[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[3,4,5,6,2,7,1,8]=>0000001 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[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>[6,5,7,1,2,3,4,8]=>0000001 [[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>[5,6,7,1,2,3,4,8]=>0000001 [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[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]=>[4,3,2,6,7,1,5,8]=>0000001 [[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[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]=>[3,7,2,6,1,4,5,8]=>0000001 [[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>[6,7,1,2,3,4,5,8]=>0000001 [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[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]=>[4,5,3,2,7,1,6,8]=>0000001 [[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>[4,5,2,3,7,1,6,8]=>0000001 [[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>[3,5,2,4,7,1,6,8]=>0000001 [[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]=>[5,4,3,7,1,2,6,8]=>0000001 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[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>[3,2,4,6,1,5,7,8]=>0000011 [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[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]=>[4,5,3,2,1,6,7,8]=>0000111 [[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>0000111 [[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>0000111 [[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[3,4,5,2,1,6,7,8]=>0000111 [[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>0000111 [[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>[4,5,2,3,1,6,7,8]=>0000111 [[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[3,5,2,4,1,6,7,8]=>0000111 [[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>0000111 [[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>0000111 [[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>0000111 [[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[4,2,3,5,1,6,7,8]=>0000111 [[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>0000111 [[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>0000111 [[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]=>[5,4,3,1,2,6,7,8]=>0000111 [[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>[5,3,4,1,2,6,7,8]=>0000111 [[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[2,1,5,4,3,6,7,8]=>[5,2,4,1,3,6,7,8]=>0000111 [[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]=>[5,4,1,2,3,6,7,8]=>0000111 [[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,2,4,5,3,6,7,8]=>[4,5,1,2,3,6,7,8]=>0000111 [[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[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]=>[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]=>0001111 [[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>0001111 [[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>0001111 [[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>0001111 [[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>0001111 [[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[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]=>[3,4,1,2,5,6,7,8]=>0001111 [[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[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]=>[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]=>0011111 [[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>0011111 [[[[[[[.,.],[.,.]],.],.],.],.],.]=>[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]=>0111111 [[[[[[[[.,.],.],.],.],.],.],.],.]=>[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
inverse Foata bijection
Description
The inverse of Foata's 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.