Identifier
Mp00017: Binary trees to 312-avoiding permutationPermutations
Mp00073: Permutations major-index to inversion-number bijectionPermutations
Mp00061: Permutations to increasing tree Binary trees
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-3
[.,.]=>[1]=>[1]=>[.,.] [.,[.,.]]=>[2,1]=>[2,1]=>[[.,.],.] [[.,.],.]=>[1,2]=>[1,2]=>[.,[.,.]] [.,[.,[.,.]]]=>[3,2,1]=>[3,2,1]=>[[[.,.],.],.] [.,[[.,.],.]]=>[2,3,1]=>[3,1,2]=>[[.,.],[.,.]] [[.,.],[.,.]]=>[1,3,2]=>[2,3,1]=>[[.,[.,.]],.] [[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]] [[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]] [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.] [.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,3,1,2]=>[[[.,.],.],[.,.]] [.,[[.,.],[.,.]]]=>[2,4,3,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.] [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,2,1,3]=>[[[.,.],.],[.,.]] [.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,1,2,3]=>[[.,.],[.,[.,.]]] [[.,.],[.,[.,.]]]=>[1,4,3,2]=>[3,4,2,1]=>[[[.,[.,.]],.],.] [[.,.],[[.,.],.]]=>[1,3,4,2]=>[2,4,1,3]=>[[.,[.,.]],[.,.]] [[.,[.,.]],[.,.]]=>[2,1,4,3]=>[3,2,4,1]=>[[[.,.],[.,.]],.] [[[.,.],.],[.,.]]=>[1,2,4,3]=>[2,3,4,1]=>[[.,[.,[.,.]]],.] [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]] [[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]] [[[.,.],[.,.]],.]=>[1,3,2,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]] [[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.] [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]] [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.] [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]] [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]] [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.] [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]] [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.] [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.] [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]] [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]] [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]] [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]] [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]] [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.] [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]] [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.] [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[3,5,2,1,4]=>[[[.,[.,.]],.],[.,.]] [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]] [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.] [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]] [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.] [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]] [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.] [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.] [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.] [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.] [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.] [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]] [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]] [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]] [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]] [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]] [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]] [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]] [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]] [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]] [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]] [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]] [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]] [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]] [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]] [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.] [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[[[[[.,.],.],.],.],[.,.]] [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6,5,4,2,3,1]=>[[[[[.,.],.],.],[.,.]],.] [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[[[[[.,.],.],.],.],[.,.]] [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[[[[.,.],.],.],[.,[.,.]]] [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.] [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[6,5,2,4,1,3]=>[[[[.,.],.],[.,.]],[.,.]] [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,5,3,2,4,1]=>[[[[[.,.],.],.],[.,.]],.] [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,5,2,3,4,1]=>[[[[.,.],.],[.,[.,.]]],.] [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[[[[[.,.],.],.],.],[.,.]] [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[[[[.,.],.],.],[.,[.,.]]] [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[6,5,2,3,1,4]=>[[[[.,.],.],[.,.]],[.,.]] [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>[[[[.,.],.],.],[.,[.,.]]] [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>[[[.,.],.],[.,[.,[.,.]]]] [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,4,5,3,2,1]=>[[[[[.,.],[.,.]],.],.],.] [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[6,3,5,4,1,2]=>[[[.,.],[[.,.],.]],[.,.]] [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,3,5,2,4,1]=>[[[[.,.],[.,.]],[.,.]],.] [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[6,3,5,2,1,4]=>[[[[.,.],[.,.]],.],[.,.]] [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[6,2,5,1,3,4]=>[[[.,.],[.,.]],[.,[.,.]]] [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,4,3,5,2,1]=>[[[[[.,.],.],[.,.]],.],.] [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[6,3,2,5,1,4]=>[[[[.,.],.],[.,.]],[.,.]] [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,3,4,5,2,1]=>[[[[.,.],[.,[.,.]]],.],.] [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[6,2,3,5,1,4]=>[[[.,.],[.,[.,.]]],[.,.]] [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.] [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,4,2,3,5,1]=>[[[[.,.],.],[.,[.,.]]],.] [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,3,4,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.] [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.] [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.] [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],.],[.,.]] [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[[[[.,.],.],.],[.,[.,.]]] [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[6,4,2,3,1,5]=>[[[[.,.],.],[.,.]],[.,.]] [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[[[[.,.],.],.],[.,[.,.]]] [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]] [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[6,3,4,2,1,5]=>[[[[.,.],[.,.]],.],[.,.]] [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6,2,4,1,3,5]=>[[[.,.],[.,.]],[.,[.,.]]] [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[6,3,2,4,1,5]=>[[[[.,.],.],[.,.]],[.,.]] [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,.]]],[.,.]] [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]] [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>[[[.,.],.],[.,[.,[.,.]]]] [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[6,2,3,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]] [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]] [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]] [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[5,6,4,3,2,1]=>[[[[[.,[.,.]],.],.],.],.] [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[4,6,5,3,1,2]=>[[[.,[[.,.],.]],.],[.,.]] [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[4,6,5,2,3,1]=>[[[.,[[.,.],.]],[.,.]],.] [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[4,6,5,2,1,3]=>[[[.,[[.,.],.]],.],[.,.]] [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[3,6,5,1,2,4]=>[[.,[[.,.],.]],[.,[.,.]]] [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[4,6,3,5,2,1]=>[[[[.,[.,.]],[.,.]],.],.] [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[3,6,2,5,1,4]=>[[[.,[.,.]],[.,.]],[.,.]] [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[4,6,3,2,5,1]=>[[[[.,[.,.]],.],[.,.]],.] [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[3,6,2,4,5,1]=>[[[.,[.,.]],[.,[.,.]]],.] [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[4,6,3,2,1,5]=>[[[[.,[.,.]],.],.],[.,.]] [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[3,6,4,1,2,5]=>[[.,[[.,.],.]],[.,[.,.]]] [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[3,6,2,4,1,5]=>[[[.,[.,.]],[.,.]],[.,.]] [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[3,6,2,1,4,5]=>[[[.,[.,.]],.],[.,[.,.]]] [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]] [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[5,4,6,3,2,1]=>[[[[[.,.],[.,.]],.],.],.] [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[4,3,6,5,1,2]=>[[[.,.],[[.,.],.]],[.,.]] [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[4,3,6,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.] [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[4,3,6,2,1,5]=>[[[[.,.],[.,.]],.],[.,.]] [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[3,2,6,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]] [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[4,5,6,3,2,1]=>[[[[.,[.,[.,.]]],.],.],.] [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[3,4,6,5,1,2]=>[[.,[.,[[.,.],.]]],[.,.]] [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[3,4,6,2,5,1]=>[[[.,[.,[.,.]]],[.,.]],.] [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[3,4,6,2,1,5]=>[[[.,[.,[.,.]]],.],[.,.]] [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[2,3,6,1,4,5]=>[[.,[.,[.,.]]],[.,[.,.]]] [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[5,4,3,6,2,1]=>[[[[[.,.],.],[.,.]],.],.] [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[4,3,2,6,1,5]=>[[[[.,.],.],[.,.]],[.,.]] [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[5,3,4,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.] [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[4,2,3,6,1,5]=>[[[.,.],[.,[.,.]]],[.,.]] [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[4,5,3,6,2,1]=>[[[[.,[.,.]],[.,.]],.],.] [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[3,4,2,6,1,5]=>[[[.,[.,.]],[.,.]],[.,.]] [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[4,3,5,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.] [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[3,2,4,6,1,5]=>[[[.,.],[.,[.,.]]],[.,.]] [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[3,4,5,6,2,1]=>[[[.,[.,[.,[.,.]]]],.],.] [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[2,3,4,6,1,5]=>[[.,[.,[.,[.,.]]]],[.,.]] [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],[.,.]],.] [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[5,4,2,3,6,1]=>[[[[.,.],.],[.,[.,.]]],.] [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[5,3,4,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.] [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,[.,.]]],.] [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,[.,.]]]],.] [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[4,5,3,2,6,1]=>[[[[.,[.,.]],.],[.,.]],.] [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[3,5,2,4,6,1]=>[[[.,[.,.]],[.,[.,.]]],.] [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[4,3,5,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.] [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[3,4,5,2,6,1]=>[[[.,[.,[.,.]]],[.,.]],.] [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[4,3,2,5,6,1]=>[[[[.,.],.],[.,[.,.]]],.] [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[4,2,3,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.] [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[3,4,2,5,6,1]=>[[[.,[.,.]],[.,[.,.]]],.] [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[3,2,4,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.] [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.] [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]] [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>[[[[.,.],.],.],[.,[.,.]]] [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[5,4,2,3,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>[[[[.,.],.],.],[.,[.,.]]] [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[5,3,4,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]] [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[5,2,4,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]] [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]] [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[5,2,3,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]] [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[4,5,3,2,1,6]=>[[[[.,[.,.]],.],.],[.,.]] [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[3,5,4,1,2,6]=>[[.,[[.,.],.]],[.,[.,.]]] [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[3,5,2,4,1,6]=>[[[.,[.,.]],[.,.]],[.,.]] [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[3,5,2,1,4,6]=>[[[.,[.,.]],.],[.,[.,.]]] [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[4,3,5,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]] [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[3,2,5,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]] [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[3,4,5,2,1,6]=>[[[.,[.,[.,.]]],.],[.,.]] [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[2,3,5,1,4,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[4,3,2,5,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[4,2,3,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[3,4,2,5,1,6]=>[[[.,[.,.]],[.,.]],[.,.]] [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[3,2,4,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]] [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]] [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[3,4,2,1,5,6]=>[[[.,[.,.]],.],[.,[.,.]]] [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]] [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.] [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[[[[[[.,.],.],.],.],.],[.,.]] [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],.],.],.],.],[.,.]] [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]] [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]] [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[7,6,5,3,2,4,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[7,6,5,2,3,4,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]] [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[[[[[.,.],.],.],.],[.,[.,.]]] [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[7,6,5,2,3,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]] [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>[[[[[.,.],.],.],.],[.,[.,.]]] [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[7,6,3,5,4,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]] [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[7,6,3,5,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[7,6,3,5,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]] [.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[7,6,2,5,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[7,6,3,2,5,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]] [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[7,6,2,3,5,1,4]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[7,6,4,3,2,5,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[7,6,4,2,3,5,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[7,6,3,4,2,5,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[7,6,3,2,4,5,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[7,6,2,3,4,5,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],.],.],[.,.]] [.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[[[[[.,.],.],.],.],[.,[.,.]]] [.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]] [.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[[[[[.,.],.],.],.],[.,[.,.]]] [.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[7,6,3,4,2,1,5]=>[[[[[.,.],.],[.,.]],.],[.,.]] [.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[7,6,2,4,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[7,6,3,2,4,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]] [.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[7,6,2,3,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]] 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[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[7,4,6,3,5,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[7,3,6,2,5,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[7,4,6,3,2,5,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[7,3,6,2,4,5,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[7,4,6,3,2,1,5]=>[[[[[.,.],[.,.]],.],.],[.,.]] [.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[7,3,6,4,1,2,5]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[7,3,6,2,4,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[7,3,6,2,1,4,5]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[7,2,6,1,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[7,5,4,6,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] 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[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[5,7,6,3,4,2,1]=>[[[[.,[[.,.],.]],[.,.]],.],.] [[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[4,7,6,2,5,1,3]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[5,7,6,3,2,4,1]=>[[[[.,[[.,.],.]],.],[.,.]],.] [[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[4,7,6,2,3,5,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.] [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[5,7,6,3,2,1,4]=>[[[[.,[[.,.],.]],.],.],[.,.]] [[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[4,7,6,3,1,2,5]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[4,7,6,2,3,1,5]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[4,7,6,2,1,3,5]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[3,7,6,1,2,4,5]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[5,7,4,6,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.] [[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[4,7,3,6,5,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]] [[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[4,7,3,6,2,5,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[4,7,3,6,2,1,5]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[3,7,2,6,1,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[5,7,4,3,6,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.] [[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[4,7,3,2,6,1,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[4,7,3,5,6,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[3,7,2,4,6,1,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[5,7,4,3,2,6,1]=>[[[[[.,[.,.]],.],.],[.,.]],.] [[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[4,7,5,2,3,6,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.] [[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[4,7,3,5,2,6,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[4,7,3,2,5,6,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[3,7,2,4,5,6,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[5,7,4,3,2,1,6]=>[[[[[.,[.,.]],.],.],.],[.,.]] [[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[4,7,5,3,1,2,6]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[4,7,5,2,3,1,6]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[4,7,5,2,1,3,6]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[3,7,5,1,2,4,6]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[4,7,3,5,2,1,6]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[3,7,2,5,1,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[4,7,3,2,5,1,6]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[3,7,2,4,5,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[4,7,3,2,1,5,6]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[3,7,4,1,2,5,6]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[3,7,2,4,1,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[3,7,2,1,4,5,6]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.] [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[5,4,7,6,3,1,2]=>[[[[.,.],[[.,.],.]],.],[.,.]] [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[5,4,7,6,2,3,1]=>[[[[.,.],[[.,.],.]],[.,.]],.] [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[5,4,7,6,2,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]] [[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[4,3,7,6,1,2,5]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[5,4,7,3,6,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[4,3,7,2,6,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[5,4,7,3,2,6,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[4,3,7,2,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[5,4,7,3,2,1,6]=>[[[[[.,.],[.,.]],.],.],[.,.]] [[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[4,3,7,5,1,2,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[4,3,7,2,5,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[4,3,7,2,1,5,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[3,2,7,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[5,6,7,4,3,2,1]=>[[[[[.,[.,[.,.]]],.],.],.],.] [[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[4,5,7,6,3,1,2]=>[[[.,[.,[[.,.],.]]],.],[.,.]] [[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[4,5,7,6,2,3,1]=>[[[.,[.,[[.,.],.]]],[.,.]],.] [[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[4,5,7,6,2,1,3]=>[[[.,[.,[[.,.],.]]],.],[.,.]] [[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[3,4,7,6,1,2,5]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[4,5,7,3,6,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.] [[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[3,4,7,2,6,1,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[4,5,7,3,2,6,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.] [[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[3,4,7,2,5,6,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.] [[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[4,5,7,3,2,1,6]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[3,4,7,5,1,2,6]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[3,4,7,2,5,1,6]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[3,4,7,2,1,5,6]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[2,3,7,1,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[5,4,3,7,6,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]] [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[5,4,3,7,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[5,4,3,7,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]] [[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[4,3,2,7,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[6,4,5,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.] [[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[5,3,4,7,6,1,2]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[5,3,4,7,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[5,3,4,7,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[4,2,3,7,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[5,6,4,7,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.] [[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[4,5,3,7,6,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]] [[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[4,5,3,7,2,6,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[4,5,3,7,2,1,6]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[3,4,2,7,1,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[5,4,6,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.] [[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[4,3,5,7,6,1,2]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[4,3,5,7,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[4,3,5,7,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[3,2,4,7,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>[[[[.,[.,[.,[.,.]]]],.],.],.] [[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[3,4,5,7,6,1,2]=>[[.,[.,[.,[[.,.],.]]]],[.,.]] [[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[3,4,5,7,2,6,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.] [[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[3,4,5,7,2,1,6]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[2,3,4,7,1,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[5,4,3,2,7,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[6,5,3,4,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[5,4,2,3,7,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[6,4,5,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[5,3,4,2,7,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[6,4,3,5,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[5,3,2,4,7,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[6,3,4,5,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[5,2,3,4,7,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[5,6,4,3,7,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.] [[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[4,5,3,2,7,1,6]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[4,6,3,5,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[3,5,2,4,7,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[5,4,6,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[4,3,5,2,7,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[4,5,6,3,7,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.] [[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[3,4,5,2,7,1,6]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[4,3,2,5,7,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]] 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[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]] [[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[6,5,4,2,3,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[6,5,2,4,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[6,5,3,2,4,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[6,5,2,3,4,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[6,5,2,3,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[6,4,5,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]] [[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[6,3,5,4,1,2,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[6,3,5,2,4,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[6,3,5,2,1,4,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[6,2,5,1,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[6,4,3,5,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[6,3,2,5,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[6,3,4,5,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[6,2,3,5,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[6,4,2,3,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[6,3,4,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[6,4,2,3,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[6,3,4,2,1,5,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[6,2,4,1,3,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[6,3,2,4,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[5,6,4,3,2,1,7]=>[[[[[.,[.,.]],.],.],.],[.,.]] [[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[4,6,5,3,1,2,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[4,6,5,2,3,1,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[4,6,5,2,1,3,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[3,6,5,1,2,4,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[4,6,3,5,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[3,6,2,5,1,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[4,6,3,2,5,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[3,6,2,4,5,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[4,6,3,2,1,5,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[3,6,4,1,2,5,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[3,6,2,4,1,5,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[3,6,2,1,4,5,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[2,6,1,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[5,4,6,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]] [[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[4,3,6,5,1,2,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[4,3,6,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[4,3,6,2,1,5,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[3,2,6,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[4,5,6,3,2,1,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[3,4,6,5,1,2,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[3,4,6,2,5,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[3,4,6,2,1,5,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[2,3,6,1,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[4,3,2,6,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[5,3,4,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[4,2,3,6,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[4,5,3,6,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[3,4,2,6,1,5,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[4,3,5,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[3,2,4,6,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[3,4,5,6,2,1,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[2,3,4,6,1,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[5,4,2,3,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[5,3,4,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[4,5,3,2,6,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[3,5,2,4,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[4,3,5,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[3,4,5,2,6,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[3,4,2,5,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[5,4,2,3,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[5,3,4,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[5,2,4,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[4,5,3,2,1,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[3,5,4,1,2,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[3,5,2,4,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[3,5,2,1,4,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[2,5,1,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[4,3,5,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[3,2,5,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[3,4,5,2,1,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[2,3,5,1,4,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[3,4,2,5,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[3,2,4,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[3,4,2,1,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[2,4,1,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[3,2,4,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.] [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
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
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.