Identifier
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00277: Permutations —catalanization⟶ Permutations
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1] [.,[.,.]]=>[2,1]=>[2,1] [[.,.],.]=>[1,2]=>[1,2] [.,[.,[.,.]]]=>[3,2,1]=>[3,2,1] [.,[[.,.],.]]=>[2,3,1]=>[2,3,1] [[.,.],[.,.]]=>[1,3,2]=>[1,3,2] [[.,[.,.]],.]=>[2,1,3]=>[2,1,3] [[[.,.],.],.]=>[1,2,3]=>[1,2,3] [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1] [.,[.,[[.,.],.]]]=>[3,4,2,1]=>[3,4,2,1] [.,[[.,.],[.,.]]]=>[2,4,3,1]=>[2,4,3,1] [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[3,2,4,1] [.,[[[.,.],.],.]]=>[2,3,4,1]=>[2,3,4,1] [[.,.],[.,[.,.]]]=>[1,4,3,2]=>[1,4,3,2] [[.,.],[[.,.],.]]=>[1,3,4,2]=>[1,3,4,2] [[.,[.,.]],[.,.]]=>[2,1,4,3]=>[2,1,4,3] [[[.,.],.],[.,.]]=>[1,2,4,3]=>[1,2,4,3] [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4] [[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,3,1,4] [[[.,.],[.,.]],.]=>[1,3,2,4]=>[1,3,2,4] [[[.,[.,.]],.],.]=>[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]=>[4,5,3,2,1] [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[3,5,4,2,1] [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[4,3,5,2,1] [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,4,5,2,1] [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[2,5,4,3,1] [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[2,4,5,3,1] [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[3,2,5,4,1] [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[2,3,5,4,1] [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[4,3,2,5,1] [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,4,2,5,1] [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[2,4,3,5,1] [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,2,4,5,1] [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[2,3,4,5,1] [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[1,5,4,3,2] [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[1,4,5,3,2] [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[1,3,5,4,2] [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[1,4,3,5,2] [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[1,3,4,5,2] [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[2,1,5,4,3] [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[2,1,4,5,3] [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[1,2,5,4,3] [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[1,2,4,5,3] [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[3,2,1,5,4] [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[2,3,1,5,4] [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[1,3,2,5,4] [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[2,1,3,5,4] [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[1,2,3,5,4] [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5] [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[3,4,2,1,5] [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[2,4,3,1,5] [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,2,4,1,5] [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[2,3,4,1,5] [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[1,4,3,2,5] [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[1,3,4,2,5] [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[2,1,4,3,5] [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[1,2,4,3,5] [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5] [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,3,1,4,5] [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[1,3,2,4,5] [[[[.,[.,.]],.],.],.]=>[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]=>[5,6,4,3,2,1] [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[4,6,5,3,2,1] [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[5,4,6,3,2,1] [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[4,5,6,3,2,1] [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[3,6,5,4,2,1] [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[3,5,6,4,2,1] [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[4,3,6,5,2,1] [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[3,4,6,5,2,1] [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[5,4,3,6,2,1] [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[4,5,3,6,2,1] [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[3,5,4,6,2,1] [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[4,3,5,6,2,1] [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[3,4,5,6,2,1] [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[2,6,5,4,3,1] [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[2,5,6,4,3,1] [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[2,4,6,5,3,1] [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[2,5,4,6,3,1] [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[2,4,5,6,3,1] [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[3,2,6,5,4,1] [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[3,2,5,6,4,1] [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[2,3,6,5,4,1] [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[2,3,5,6,4,1] [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[4,3,2,6,5,1] [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[3,4,2,6,5,1] [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[2,4,3,6,5,1] [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[3,2,4,6,5,1] [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[2,3,4,6,5,1] [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1] [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[4,5,3,2,6,1] [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[3,5,4,2,6,1] [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[4,3,5,2,6,1] [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,4,5,2,6,1] [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[2,5,4,3,6,1] [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[2,4,5,3,6,1] [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[3,2,5,4,6,1] [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[2,3,5,4,6,1] [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1] [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[3,4,2,5,6,1] [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[2,4,3,5,6,1] [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1] [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1] [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[1,6,5,4,3,2] [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[1,5,6,4,3,2] [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[1,4,6,5,3,2] [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[1,5,4,6,3,2] [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[1,4,5,6,3,2] [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[1,3,6,5,4,2] [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[1,3,5,6,4,2] [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[1,4,3,6,5,2] [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[1,3,4,6,5,2] [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[1,5,4,3,6,2] [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[1,4,5,3,6,2] [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[1,3,5,4,6,2] [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[1,4,3,5,6,2] [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[1,3,4,5,6,2] [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[2,1,6,5,4,3] [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[2,1,5,6,4,3] [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[2,1,4,6,5,3] [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[2,1,5,4,6,3] [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[2,1,4,5,6,3] [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[1,2,6,5,4,3] [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[1,2,5,6,4,3] [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[1,2,4,6,5,3] [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[1,2,5,4,6,3] [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[1,2,4,5,6,3] [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4] [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[3,2,1,5,6,4] [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[2,3,1,6,5,4] [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[2,3,1,5,6,4] [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[1,3,2,6,5,4] [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[1,3,2,5,6,4] [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[2,1,3,6,5,4] [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[2,1,3,5,6,4] [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[1,2,3,6,5,4] [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[1,2,3,5,6,4] [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5] [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[3,4,2,1,6,5] [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[2,4,3,1,6,5] [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[3,2,4,1,6,5] [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[2,3,4,1,6,5] [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[1,4,3,2,6,5] [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[1,3,4,2,6,5] [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5] [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5] [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[3,2,1,4,6,5] [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[2,3,1,4,6,5] [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5] [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5] [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5] [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6] [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[4,5,3,2,1,6] [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[3,5,4,2,1,6] [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[4,3,5,2,1,6] [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,4,5,2,1,6] [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[2,5,4,3,1,6] [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[2,4,5,3,1,6] [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[3,2,5,4,1,6] [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[2,3,5,4,1,6] [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[4,3,2,5,1,6] [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[3,4,2,5,1,6] [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[2,4,3,5,1,6] [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[3,2,4,5,1,6] [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[2,3,4,5,1,6] [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[1,5,4,3,2,6] [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[1,4,5,3,2,6] [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[1,3,5,4,2,6] [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[1,4,3,5,2,6] [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[1,3,4,5,2,6] [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[2,1,5,4,3,6] [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[2,1,4,5,3,6] [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[1,2,5,4,3,6] [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[1,2,4,5,3,6] [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[3,2,1,5,4,6] [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[2,3,1,5,4,6] [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6] [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6] [[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6] [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6] [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[3,4,2,1,5,6] [[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[2,4,3,1,5,6] [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[3,2,4,1,5,6] [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[2,3,4,1,5,6] [[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[1,4,3,2,5,6] [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[1,3,4,2,5,6] [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6] [[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6] [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6] [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[2,3,1,4,5,6] [[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6] [[[[[.,[.,.]],.],.],.],.]=>[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]=>[6,7,5,4,3,2,1] [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[5,7,6,4,3,2,1] [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[6,5,7,4,3,2,1] [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[5,6,7,4,3,2,1] [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[4,7,6,5,3,2,1] [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[4,6,7,5,3,2,1] [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[5,4,7,6,3,2,1] [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[4,5,7,6,3,2,1] [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[6,5,4,7,3,2,1] [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[5,6,4,7,3,2,1] [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[4,6,5,7,3,2,1] [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[5,4,6,7,3,2,1] [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,5,6,7,3,2,1] [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[3,7,6,5,4,2,1] [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[3,6,7,5,4,2,1] [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[3,5,7,6,4,2,1] [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[3,6,5,7,4,2,1] [.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[3,5,6,7,4,2,1] [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[4,3,7,6,5,2,1] [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[4,3,6,7,5,2,1] [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[3,4,7,6,5,2,1] [.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[3,4,6,7,5,2,1] [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[5,4,3,7,6,2,1] [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[4,5,3,7,6,2,1] [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[3,5,4,7,6,2,1] [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[4,3,5,7,6,2,1] [.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[3,4,5,7,6,2,1] [.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[6,5,4,3,7,2,1] [.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[5,6,4,3,7,2,1] [.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[4,6,5,3,7,2,1] [.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[5,4,6,3,7,2,1] [.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[4,5,6,3,7,2,1] [.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[3,6,5,4,7,2,1] [.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[3,5,6,4,7,2,1] [.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[4,3,6,5,7,2,1] [.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[3,4,6,5,7,2,1] [.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[5,4,3,6,7,2,1] [.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[4,5,3,6,7,2,1] [.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[3,5,4,6,7,2,1] [.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[4,3,5,6,7,2,1] [.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[3,4,5,6,7,2,1] [.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[2,7,6,5,4,3,1] [.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[2,6,7,5,4,3,1] [.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[2,5,7,6,4,3,1] [.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[2,6,5,7,4,3,1] [.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[2,5,6,7,4,3,1] [.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[2,4,7,6,5,3,1] [.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[2,4,6,7,5,3,1] [.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[2,5,4,7,6,3,1] [.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[2,4,5,7,6,3,1] [.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[2,6,5,4,7,3,1] [.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[2,5,6,4,7,3,1] [.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[2,4,6,5,7,3,1] [.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[2,5,4,6,7,3,1] [.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[2,4,5,6,7,3,1] [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[3,2,7,6,5,4,1] [.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[3,2,6,7,5,4,1] [.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[3,2,5,7,6,4,1] [.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[3,2,6,5,7,4,1] [.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[3,2,5,6,7,4,1] [.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[2,3,7,6,5,4,1] [.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[2,3,6,7,5,4,1] [.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[2,3,5,7,6,4,1] [.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[2,3,6,5,7,4,1] [.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[2,3,5,6,7,4,1] [.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[4,3,2,7,6,5,1] [.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[4,3,2,6,7,5,1] [.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[3,4,2,7,6,5,1] [.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[3,4,2,6,7,5,1] [.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[2,4,3,7,6,5,1] [.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[2,4,3,6,7,5,1] [.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[3,2,4,7,6,5,1] [.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[3,2,4,6,7,5,1] [.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[2,3,4,7,6,5,1] [.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[2,3,4,6,7,5,1] [.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[5,4,3,2,7,6,1] [.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[4,5,3,2,7,6,1] [.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[3,5,4,2,7,6,1] [.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[4,3,5,2,7,6,1] [.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[3,4,5,2,7,6,1] [.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[2,5,4,3,7,6,1] [.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[2,4,5,3,7,6,1] [.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[3,2,5,4,7,6,1] [.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[2,3,5,4,7,6,1] [.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[4,3,2,5,7,6,1] [.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[3,4,2,5,7,6,1] [.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[2,4,3,5,7,6,1] [.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[3,2,4,5,7,6,1] [.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[2,3,4,5,7,6,1] [.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[6,5,4,3,2,7,1] [.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[5,6,4,3,2,7,1] [.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[4,6,5,3,2,7,1] [.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[5,4,6,3,2,7,1] [.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[4,5,6,3,2,7,1] [.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[3,6,5,4,2,7,1] [.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[3,5,6,4,2,7,1] [.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[4,3,6,5,2,7,1] [.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[3,4,6,5,2,7,1] [.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[5,4,3,6,2,7,1] [.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[4,5,3,6,2,7,1] [.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[3,5,4,6,2,7,1] [.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[4,3,5,6,2,7,1] [.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[3,4,5,6,2,7,1] [.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[2,6,5,4,3,7,1] [.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[2,5,6,4,3,7,1] [.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[2,4,6,5,3,7,1] [.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[2,5,4,6,3,7,1] [.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[2,4,5,6,3,7,1] [.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[3,2,6,5,4,7,1] [.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[3,2,5,6,4,7,1] [.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[2,3,6,5,4,7,1] [.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[2,3,5,6,4,7,1] [.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[4,3,2,6,5,7,1] [.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[3,4,2,6,5,7,1] [.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[2,4,3,6,5,7,1] [.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[3,2,4,6,5,7,1] [.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[2,3,4,6,5,7,1] [.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[5,4,3,2,6,7,1] [.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[4,5,3,2,6,7,1] [.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[3,5,4,2,6,7,1] [.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[4,3,5,2,6,7,1] [.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[3,4,5,2,6,7,1] [.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[2,5,4,3,6,7,1] [.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[2,4,5,3,6,7,1] [.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[3,2,5,4,6,7,1] [.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[2,3,5,4,6,7,1] [.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[4,3,2,5,6,7,1] [.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[3,4,2,5,6,7,1] [.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[2,4,3,5,6,7,1] [.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[3,2,4,5,6,7,1] [.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,7,1] [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2] [[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[1,6,7,5,4,3,2] [[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[1,5,7,6,4,3,2] [[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[1,6,5,7,4,3,2] [[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[1,5,6,7,4,3,2] [[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[1,4,7,6,5,3,2] [[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[1,4,6,7,5,3,2] [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[1,5,4,7,6,3,2] [[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[1,4,5,7,6,3,2] [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[1,6,5,4,7,3,2] [[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[1,5,6,4,7,3,2] [[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[1,4,6,5,7,3,2] [[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[1,5,4,6,7,3,2] [[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[1,4,5,6,7,3,2] [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[1,3,7,6,5,4,2] [[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[1,3,6,7,5,4,2] [[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[1,3,5,7,6,4,2] [[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[1,3,6,5,7,4,2] [[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[1,3,5,6,7,4,2] [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[1,4,3,7,6,5,2] [[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[1,4,3,6,7,5,2] [[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[1,3,4,7,6,5,2] [[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[1,3,4,6,7,5,2] [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[1,5,4,3,7,6,2] [[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[1,4,5,3,7,6,2] [[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[1,3,5,4,7,6,2] [[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[1,4,3,5,7,6,2] [[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[1,3,4,5,7,6,2] [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[1,6,5,4,3,7,2] [[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[1,5,6,4,3,7,2] [[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[1,4,6,5,3,7,2] [[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[1,5,4,6,3,7,2] [[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[1,4,5,6,3,7,2] [[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[1,3,6,5,4,7,2] [[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[1,3,5,6,4,7,2] [[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[1,4,3,6,5,7,2] [[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[1,3,4,6,5,7,2] [[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[1,5,4,3,6,7,2] [[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[1,4,5,3,6,7,2] [[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[1,3,5,4,6,7,2] [[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[1,4,3,5,6,7,2] [[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[1,3,4,5,6,7,2] [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3] [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[2,1,6,7,5,4,3] [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[2,1,5,7,6,4,3] [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[2,1,6,5,7,4,3] [[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[2,1,5,6,7,4,3] [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[2,1,4,7,6,5,3] [[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[2,1,4,6,7,5,3] [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[2,1,5,4,7,6,3] [[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[2,1,4,5,7,6,3] [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[2,1,6,5,4,7,3] [[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[2,1,5,6,4,7,3] [[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[2,1,4,6,5,7,3] [[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[2,1,5,4,6,7,3] [[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[2,1,4,5,6,7,3] [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[1,2,7,6,5,4,3] [[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[1,2,6,7,5,4,3] [[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[1,2,5,7,6,4,3] [[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[1,2,6,5,7,4,3] [[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[1,2,5,6,7,4,3] [[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[1,2,4,7,6,5,3] [[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[1,2,4,6,7,5,3] [[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[1,2,5,4,7,6,3] [[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[1,2,4,5,7,6,3] [[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[1,2,6,5,4,7,3] [[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[1,2,5,6,4,7,3] [[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[1,2,4,6,5,7,3] [[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[1,2,5,4,6,7,3] [[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[1,2,4,5,6,7,3] [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4] [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[3,2,1,6,7,5,4] [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[3,2,1,5,7,6,4] [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[3,2,1,6,5,7,4] [[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[3,2,1,5,6,7,4] [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[2,3,1,7,6,5,4] [[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[2,3,1,6,7,5,4] [[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[2,3,1,5,7,6,4] [[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[2,3,1,6,5,7,4] [[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[2,3,1,5,6,7,4] [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[1,3,2,7,6,5,4] [[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[1,3,2,6,7,5,4] [[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[1,3,2,5,7,6,4] [[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[1,3,2,6,5,7,4] [[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[1,3,2,5,6,7,4] [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[2,1,3,7,6,5,4] [[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[2,1,3,6,7,5,4] [[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[2,1,3,5,7,6,4] [[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[2,1,3,6,5,7,4] [[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[2,1,3,5,6,7,4] [[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[1,2,3,7,6,5,4] [[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[1,2,3,6,7,5,4] [[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[1,2,3,5,7,6,4] [[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[1,2,3,6,5,7,4] [[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[1,2,3,5,6,7,4] [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5] [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[4,3,2,1,6,7,5] [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[3,4,2,1,7,6,5] [[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[3,4,2,1,6,7,5] [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[2,4,3,1,7,6,5] [[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[2,4,3,1,6,7,5] [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[3,2,4,1,7,6,5] [[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[3,2,4,1,6,7,5] [[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[2,3,4,1,7,6,5] [[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[2,3,4,1,6,7,5] [[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[1,4,3,2,7,6,5] [[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[1,4,3,2,6,7,5] [[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[1,3,4,2,7,6,5] [[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[1,3,4,2,6,7,5] [[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,7,6,5] [[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[2,1,4,3,6,7,5] [[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,7,6,5] [[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[1,2,4,3,6,7,5] [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[3,2,1,4,7,6,5] [[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[3,2,1,4,6,7,5] [[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[2,3,1,4,7,6,5] [[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[2,3,1,4,6,7,5] [[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,7,6,5] [[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[1,3,2,4,6,7,5] [[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,7,6,5] [[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[2,1,3,4,6,7,5] [[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,7,6,5] [[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[1,2,3,4,6,7,5] [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6] [[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[4,5,3,2,1,7,6] [[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[3,5,4,2,1,7,6] [[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[4,3,5,2,1,7,6] [[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[3,4,5,2,1,7,6] [[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[2,5,4,3,1,7,6] [[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[2,4,5,3,1,7,6] [[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[3,2,5,4,1,7,6] [[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[2,3,5,4,1,7,6] [[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[4,3,2,5,1,7,6] [[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[3,4,2,5,1,7,6] [[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[2,4,3,5,1,7,6] [[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[3,2,4,5,1,7,6] [[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[2,3,4,5,1,7,6] [[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[1,5,4,3,2,7,6] [[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[1,4,5,3,2,7,6] [[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[1,3,5,4,2,7,6] [[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[1,4,3,5,2,7,6] [[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[1,3,4,5,2,7,6] [[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[2,1,5,4,3,7,6] [[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[2,1,4,5,3,7,6] 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[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7] [[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[3,2,1,4,6,5,7] [[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[2,3,1,4,6,5,7] [[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7] [[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7] [[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7] [[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7] [[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[4,5,3,2,1,6,7] [[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[3,5,4,2,1,6,7] [[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[4,3,5,2,1,6,7] [[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[3,4,5,2,1,6,7] [[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[2,5,4,3,1,6,7] [[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[2,4,5,3,1,6,7] [[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[3,2,5,4,1,6,7] [[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[2,3,5,4,1,6,7] [[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6,7] [[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[3,4,2,5,1,6,7] [[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[2,4,3,5,1,6,7] [[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6,7] [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6,7] [[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[1,5,4,3,2,6,7] [[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[1,4,5,3,2,6,7] [[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[1,3,5,4,2,6,7] [[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[1,4,3,5,2,6,7] [[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[1,3,4,5,2,6,7] [[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[2,1,5,4,3,6,7] [[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[2,1,4,5,3,6,7] [[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[1,2,5,4,3,6,7] [[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[1,2,4,5,3,6,7] [[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[3,2,1,5,4,6,7] [[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[2,3,1,5,4,6,7] [[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7] [[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7] [[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7] [[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7] [[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[3,4,2,1,5,6,7] [[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[2,4,3,1,5,6,7] [[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[3,2,4,1,5,6,7] [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6,7] [[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[1,4,3,2,5,6,7] [[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[1,3,4,2,5,6,7] [[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7] [[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7] [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7] [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[2,3,1,4,5,6,7] [[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7] [[[[[[.,[.,.]],.],.],.],.],.]=>[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] [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[5,6,7,8,4,3,2,1] [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[3,5,8,7,6,4,2,1] [.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[3,5,6,7,8,4,2,1] [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>[2,6,8,7,5,4,3,1] [.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[2,5,6,7,8,4,3,1] [.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>[2,3,5,6,8,7,4,1] [.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[2,3,5,6,7,8,4,1] [.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[3,4,2,5,7,8,6,1]=>[3,4,2,5,7,8,6,1] [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[5,4,6,3,7,2,8,1] [.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[4,3,6,5,7,2,8,1] [.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[3,2,6,5,7,4,8,1] [.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[4,3,5,2,7,6,8,1] [.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[3,2,5,4,7,6,8,1] [.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,8,1] [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2] [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[1,7,8,6,5,4,3,2] [[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[1,5,6,7,8,4,3,2] [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[1,3,5,7,8,6,4,2] [[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[1,3,5,6,7,8,4,2] [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[1,4,3,8,7,6,5,2] [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>[1,6,5,4,3,8,7,2] [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[1,4,3,6,5,8,7,2] [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3] [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[2,1,6,7,8,5,4,3] [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[2,1,6,7,5,8,4,3] [[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[2,1,5,6,7,8,4,3] [[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[2,1,6,5,7,4,8,3] [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[2,1,5,4,7,6,8,3] [[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[2,1,4,5,6,7,8,3] [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[1,2,6,7,8,5,4,3] [[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[1,2,5,6,7,8,4,3] [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4] [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[3,2,1,6,5,8,7,4] [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[1,2,3,5,6,7,8,4] [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5] [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[4,3,2,1,7,8,6,5] [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[4,3,2,1,6,8,7,5] [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[4,3,2,1,7,6,8,5] [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[4,3,2,1,6,7,8,5] [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[3,4,2,1,8,7,6,5] [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[3,4,2,1,7,8,6,5] [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[2,4,3,1,8,7,6,5] [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[2,4,3,1,6,8,7,5] [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[2,4,3,1,7,6,8,5] [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[3,2,4,1,8,7,6,5] [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[3,2,4,1,6,8,7,5] [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[3,2,4,1,7,6,8,5] [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[2,3,4,1,8,7,6,5] [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[2,3,4,1,6,7,8,5] [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[1,4,3,2,8,7,6,5] [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[1,3,4,2,8,7,6,5] [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,7,6,5] [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,7,8,6,5] [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,6,8,7,5] [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,7,6,8,5] [[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,6,7,8,5] [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,7,6,5] [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[3,2,1,4,8,7,6,5] [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[2,3,1,4,8,7,6,5] [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,7,6,5] [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,7,6,5] [[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,7,6,5] [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6] [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>[3,2,5,4,1,8,7,6] [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,5,8,7,6] [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[4,3,2,1,5,7,8,6] [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[3,2,1,4,5,8,7,6] [[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[2,3,1,4,5,7,8,6] [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7] [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[4,5,6,3,2,1,8,7] [[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[4,5,3,6,2,1,8,7] [[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[4,3,5,2,6,1,8,7] [[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[3,2,5,4,6,1,8,7] [[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[2,3,4,5,6,1,8,7] [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,8,7] [[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[2,1,5,6,4,3,8,7] [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[2,1,4,6,5,3,8,7] [[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[2,1,5,4,6,3,8,7] [[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[2,1,4,5,6,3,8,7] [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7] [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[3,4,2,1,6,5,8,7] [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[2,4,3,1,6,5,8,7] [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[3,2,4,1,6,5,8,7] [[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[2,3,4,1,6,5,8,7] [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7] [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,5,6,8,7] [[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7] [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8] [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[3,2,7,6,5,4,1,8] [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>[5,4,3,2,7,6,1,8] [[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[3,2,5,4,7,6,1,8] [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5,8] [[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[4,3,2,1,6,7,5,8] [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[1,4,3,2,7,6,5,8] [[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[1,3,4,2,6,7,5,8] [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,5,7,6,8] [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8] [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7,8] [[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8] [[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8] [[[[[[[[.,.],.],.],.],.],.],.],.]=>[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
catalanization
Description
The catalanization of a permutation.
For a permutation $\sigma$, this is the product of the reflections corresponding to the inversions of $\sigma$ in lex-order.
A permutation is $231$-avoiding if and only if it is a fixpoint of this map. Also, for every permutation there exists an index $k$ such that the $k$-fold application of this map is $231$-avoiding.