Identifier
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
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]=>[2,3,1]=>[[.,[.,.]],.] [[.,.],[.,.]]=>[1,3,2]=>[3,1,2]=>[[.,.],[.,.]] [[.,[.,.]],.]=>[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]=>[4,2,3,1]=>[[[.,.],[.,.]],.] [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[3,2,4,1]=>[[[.,.],[.,.]],.] [.,[[[.,.],.],.]]=>[2,3,4,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.] [[.,.],[.,[.,.]]]=>[1,4,3,2]=>[4,3,1,2]=>[[[.,.],.],[.,.]] [[.,.],[[.,.],.]]=>[1,3,4,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]] [[.,[.,.]],[.,.]]=>[2,1,4,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]] [[[.,.],.],[.,.]]=>[1,2,4,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]] [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]] [[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]] [[[.,.],[.,.]],.]=>[1,3,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]] [[[.,[.,.]],.],.]=>[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]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.] [.,[.,[[.,[.,.]],.]]]=>[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]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.] [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.] [.,[[.,[.,.]],[.,.]]]=>[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]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.] [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.] [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.] [.,[[[.,[.,.]],.],.]]=>[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]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]] [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[4,5,1,3,2]=>[[.,[.,.]],[[.,.],.]] [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[5,3,1,4,2]=>[[[.,.],.],[[.,.],.]] [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]] [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]] [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]] [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[4,2,1,5,3]=>[[[.,.],.],[[.,.],.]] [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]] [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]] [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]] [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]] [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]] [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]] [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]] [[.,[.,[.,[.,.]]]],.]=>[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]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]] [[.,[[.,[.,.]],.]],.]=>[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]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]] [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]] [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]] [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]] [[[.,[.,[.,.]]],.],.]=>[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]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]] [[[[.,[.,.]],.],.],.]=>[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]=>[6,4,5,3,2,1]=>[[[[[.,.],[.,.]],.],.],.] [.,[.,[.,[[.,[.,.]],.]]]]=>[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]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.] [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[5,3,6,4,2,1]=>[[[[.,.],[[.,.],.]],.],.] [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,4,3,5,2,1]=>[[[[[.,.],.],[.,.]],.],.] [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,3,4,5,2,1]=>[[[[.,.],[.,[.,.]]],.],.] [.,[.,[[.,[.,[.,.]]],.]]]=>[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]=>[5,3,4,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.] [.,[.,[[[.,[.,.]],.],.]]]=>[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]=>[6,5,4,2,3,1]=>[[[[[.,.],.],.],[.,.]],.] [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[5,6,2,4,3,1]=>[[[.,[.,.]],[[.,.],.]],.] [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,4,2,5,3,1]=>[[[[.,.],.],[[.,.],.]],.] [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[5,4,2,6,3,1]=>[[[[.,.],.],[[.,.],.]],.] [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[4,2,5,6,3,1]=>[[[.,.],[[.,[.,.]],.]],.] [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,5,3,2,4,1]=>[[[[[.,.],.],.],[.,.]],.] [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[5,3,2,6,4,1]=>[[[[.,.],.],[[.,.],.]],.] [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,5,2,3,4,1]=>[[[[.,.],.],[.,[.,.]]],.] [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[5,2,3,6,4,1]=>[[[.,.],[.,[[.,.],.]]],.] [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.] [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,3,4,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.] [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,4,2,3,5,1]=>[[[[.,.],.],[.,[.,.]]],.] [.,[[[.,[.,.]],.],[.,.]]]=>[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]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],[.,.]],.] [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[4,5,3,2,6,1]=>[[[[.,[.,.]],.],[.,.]],.] [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[5,3,4,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.] [.,[[.,[[.,[.,.]],.]],.]]=>[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]=>[5,4,2,3,6,1]=>[[[[.,.],.],[.,[.,.]]],.] [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[4,2,5,3,6,1]=>[[[.,.],[[.,.],[.,.]]],.] [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,[.,.]]],.] [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,[.,.]]]],.] [.,[[[.,[.,[.,.]]],.],.]]=>[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]=>[4,2,3,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.] [.,[[[[.,[.,.]],.],.],.]]=>[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]=>[6,5,4,3,1,2]=>[[[[[.,.],.],.],.],[.,.]] [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[5,6,4,1,3,2]=>[[[.,[.,.]],.],[[.,.],.]] [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[6,4,5,1,3,2]=>[[[.,.],[.,.]],[[.,.],.]] [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[5,4,6,1,3,2]=>[[[.,.],[.,.]],[[.,.],.]] [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[4,5,1,6,3,2]=>[[.,[.,.]],[[[.,.],.],.]] [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[6,5,3,1,4,2]=>[[[[.,.],.],.],[[.,.],.]] [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[5,3,1,6,4,2]=>[[[.,.],.],[[[.,.],.],.]] [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[6,4,3,1,5,2]=>[[[[.,.],.],.],[[.,.],.]] [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[6,3,1,4,5,2]=>[[[.,.],.],[[.,[.,.]],.]] [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[5,4,3,1,6,2]=>[[[[.,.],.],.],[[.,.],.]] [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[4,5,1,3,6,2]=>[[.,[.,.]],[[.,[.,.]],.]] [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[5,3,1,4,6,2]=>[[[.,.],.],[[.,[.,.]],.]] [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[4,3,1,5,6,2]=>[[[.,.],.],[[.,[.,.]],.]] [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[3,1,4,5,6,2]=>[[.,.],[[.,[.,[.,.]]],.]] [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[6,5,4,2,1,3]=>[[[[[.,.],.],.],.],[.,.]] [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[5,6,2,1,4,3]=>[[[.,[.,.]],.],[[.,.],.]] [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[6,4,2,1,5,3]=>[[[[.,.],.],.],[[.,.],.]] [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[5,4,2,1,6,3]=>[[[[.,.],.],.],[[.,.],.]] [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[4,2,1,5,6,3]=>[[[.,.],.],[[.,[.,.]],.]] [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>[[[[.,.],.],.],[.,[.,.]]] [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[5,6,1,2,4,3]=>[[.,[.,.]],[.,[[.,.],.]]] [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[6,4,1,2,5,3]=>[[[.,.],.],[.,[[.,.],.]]] [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[5,4,1,2,6,3]=>[[[.,.],.],[.,[[.,.],.]]] [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[4,1,2,5,6,3]=>[[.,.],[.,[[.,[.,.]],.]]] [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[6,5,3,2,1,4]=>[[[[[.,.],.],.],.],[.,.]] [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[5,3,2,1,6,4]=>[[[[.,.],.],.],[[.,.],.]] [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[6,5,2,3,1,4]=>[[[[.,.],.],[.,.]],[.,.]] [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[5,2,3,1,6,4]=>[[[.,.],[.,.]],[[.,.],.]] [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]=>[[[[.,.],.],.],[.,[.,.]]] [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[5,3,1,2,6,4]=>[[[.,.],.],[.,[[.,.],.]]] [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]=>[[[[.,.],.],.],[.,[.,.]]] [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[5,2,1,3,6,4]=>[[[.,.],.],[.,[[.,.],.]]] [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>[[[.,.],.],[.,[.,[.,.]]]] [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]] [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],.],[.,.]] [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[6,3,4,2,1,5]=>[[[[.,.],[.,.]],.],[.,.]] [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[6,4,2,3,1,5]=>[[[[.,.],.],[.,.]],[.,.]] [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[6,3,2,4,1,5]=>[[[[.,.],.],[.,.]],[.,.]] [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,.]]],[.,.]] [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]=>[[[[.,.],.],.],[.,[.,.]]] [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[6,3,1,4,2,5]=>[[[.,.],.],[[.,.],[.,.]]] [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[6,4,2,1,3,5]=>[[[[.,.],.],.],[.,[.,.]]] [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]] [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]] [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[6,2,3,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]] [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[6,3,1,2,4,5]=>[[[.,.],.],[.,[.,[.,.]]]] [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]] [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]] [[.,[.,[.,[.,[.,.]]]]],.]=>[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]=>[5,3,4,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]] [[.,[.,[[.,[.,.]],.]]],.]=>[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]=>[5,4,2,3,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[4,2,5,3,1,6]=>[[[.,.],[[.,.],.]],[.,.]] [[.,[[.,[.,.]],[.,.]]],.]=>[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]=>[4,3,2,5,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[3,4,2,5,1,6]=>[[[.,[.,.]],[.,.]],[.,.]] [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[4,2,3,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [[.,[[[.,[.,.]],.],.]],.]=>[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]=>[5,4,3,1,2,6]=>[[[[.,.],.],.],[.,[.,.]]] [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[4,5,1,3,2,6]=>[[.,[.,.]],[[.,.],[.,.]]] [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[5,3,1,4,2,6]=>[[[.,.],.],[[.,.],[.,.]]] [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[4,3,1,5,2,6]=>[[[.,.],.],[[.,.],[.,.]]] [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[3,1,4,5,2,6]=>[[.,.],[[.,[.,.]],[.,.]]] [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[5,4,2,1,3,6]=>[[[[.,.],.],.],[.,[.,.]]] [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[4,2,1,5,3,6]=>[[[.,.],.],[[.,.],[.,.]]] [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]] [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]] [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[5,2,3,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]] [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[5,3,1,2,4,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[[.,[.,[.,[.,.]]]],.],.]=>[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]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [[[.,[[.,[.,.]],.]],.],.]=>[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]=>[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]] [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[[[.,[.,[.,.]]],.],.],.]=>[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]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[[[[.,[.,.]],.],.],.],.]=>[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]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.] [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[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]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[6,4,7,5,3,2,1]=>[[[[[.,.],[[.,.],.]],.],.],.] [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[7,5,4,6,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[7,4,5,6,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.] [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[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]=>[6,4,5,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.] [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[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]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[6,7,3,5,4,2,1]=>[[[[.,[.,.]],[[.,.],.]],.],.] [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[7,5,3,6,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.] [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[6,5,3,7,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.] [.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[5,3,6,7,4,2,1]=>[[[[.,.],[[.,[.,.]],.]],.],.] [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[6,4,3,7,5,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.] [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[6,3,4,7,5,2,1]=>[[[[.,.],[.,[[.,.],.]]],.],.] [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[7,4,5,3,6,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[7,4,3,5,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] 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[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[7,6,4,5,1,3,2]=>[[[[.,.],.],[.,.]],[[.,.],.]] [[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[6,4,7,1,5,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]] [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[7,5,4,6,1,3,2]=>[[[[.,.],.],[.,.]],[[.,.],.]] [[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[7,4,5,1,6,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]] [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[6,5,4,7,1,3,2]=>[[[[.,.],.],[.,.]],[[.,.],.]] [[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[5,6,4,1,7,3,2]=>[[[.,[.,.]],.],[[[.,.],.],.]] [[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[6,4,5,1,7,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]] [[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[5,4,6,1,7,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]] [[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[4,5,1,6,7,3,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]] [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[7,6,5,3,1,4,2]=>[[[[[.,.],.],.],.],[[.,.],.]] [[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[6,7,3,1,5,4,2]=>[[[.,[.,.]],.],[[[.,.],.],.]] [[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[7,5,3,1,6,4,2]=>[[[[.,.],.],.],[[[.,.],.],.]] [[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[6,5,3,1,7,4,2]=>[[[[.,.],.],.],[[[.,.],.],.]] [[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[5,3,1,6,7,4,2]=>[[[.,.],.],[[[.,[.,.]],.],.]] [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[7,6,4,3,1,5,2]=>[[[[[.,.],.],.],.],[[.,.],.]] [[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[6,4,3,1,7,5,2]=>[[[[.,.],.],.],[[[.,.],.],.]] [[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[7,6,3,1,4,5,2]=>[[[[.,.],.],.],[[.,[.,.]],.]] [[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[6,3,1,4,7,5,2]=>[[[.,.],.],[[.,[[.,.],.]],.]] [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[7,5,4,3,1,6,2]=>[[[[[.,.],.],.],.],[[.,.],.]] [[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[7,4,5,1,3,6,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[7,5,3,1,4,6,2]=>[[[[.,.],.],.],[[.,[.,.]],.]] [[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[7,4,3,1,5,6,2]=>[[[[.,.],.],.],[[.,[.,.]],.]] [[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[7,3,1,4,5,6,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[6,5,4,3,1,7,2]=>[[[[[.,.],.],.],.],[[.,.],.]] [[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[5,6,4,1,3,7,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]] [[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[6,4,5,1,3,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[5,4,6,1,3,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[4,5,1,6,3,7,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]] [[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[6,5,3,1,4,7,2]=>[[[[.,.],.],.],[[.,[.,.]],.]] [[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[5,3,1,6,4,7,2]=>[[[.,.],.],[[[.,.],[.,.]],.]] [[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[6,4,3,1,5,7,2]=>[[[[.,.],.],.],[[.,[.,.]],.]] [[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[6,3,1,4,5,7,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[5,4,3,1,6,7,2]=>[[[[.,.],.],.],[[.,[.,.]],.]] [[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[4,5,1,3,6,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[5,3,1,4,6,7,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[4,3,1,5,6,7,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[3,1,4,5,6,7,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]] [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],.],.],.],.],[.,.]] [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[6,7,5,2,1,4,3]=>[[[[.,[.,.]],.],.],[[.,.],.]] [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[7,5,6,2,1,4,3]=>[[[[.,.],[.,.]],.],[[.,.],.]] [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[6,5,7,2,1,4,3]=>[[[[.,.],[.,.]],.],[[.,.],.]] [[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[5,6,2,1,7,4,3]=>[[[.,[.,.]],.],[[[.,.],.],.]] [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[7,6,4,2,1,5,3]=>[[[[[.,.],.],.],.],[[.,.],.]] [[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[6,4,2,1,7,5,3]=>[[[[.,.],.],.],[[[.,.],.],.]] [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[7,5,4,2,1,6,3]=>[[[[[.,.],.],.],.],[[.,.],.]] [[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[7,4,2,1,5,6,3]=>[[[[.,.],.],.],[[.,[.,.]],.]] [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[6,5,4,2,1,7,3]=>[[[[[.,.],.],.],.],[[.,.],.]] [[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[5,6,2,1,4,7,3]=>[[[.,[.,.]],.],[[.,[.,.]],.]] [[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[6,4,2,1,5,7,3]=>[[[[.,.],.],.],[[.,[.,.]],.]] [[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[5,4,2,1,6,7,3]=>[[[[.,.],.],.],[[.,[.,.]],.]] [[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[4,2,1,5,6,7,3]=>[[[.,.],.],[[.,[.,[.,.]]],.]] [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[6,7,5,1,2,4,3]=>[[[.,[.,.]],.],[.,[[.,.],.]]] [[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[7,5,6,1,2,4,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[6,5,7,1,2,4,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[5,6,1,2,7,4,3]=>[[.,[.,.]],[.,[[[.,.],.],.]]] [[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[7,6,4,1,2,5,3]=>[[[[.,.],.],.],[.,[[.,.],.]]] [[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[6,4,1,2,7,5,3]=>[[[.,.],.],[.,[[[.,.],.],.]]] [[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[7,5,4,1,2,6,3]=>[[[[.,.],.],.],[.,[[.,.],.]]] [[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[7,4,1,2,5,6,3]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[6,5,4,1,2,7,3]=>[[[[.,.],.],.],[.,[[.,.],.]]] [[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[5,6,1,2,4,7,3]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[6,4,1,2,5,7,3]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[5,4,1,2,6,7,3]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[4,1,2,5,6,7,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]] [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]] [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[6,7,3,2,1,5,4]=>[[[[.,[.,.]],.],.],[[.,.],.]] [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[7,5,3,2,1,6,4]=>[[[[[.,.],.],.],.],[[.,.],.]] [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[6,5,3,2,1,7,4]=>[[[[[.,.],.],.],.],[[.,.],.]] [[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[5,3,2,1,6,7,4]=>[[[[.,.],.],.],[[.,[.,.]],.]] [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[7,6,5,2,3,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[6,7,2,3,1,5,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]] [[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[7,5,2,3,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]] [[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[6,5,2,3,1,7,4]=>[[[[.,.],.],[.,.]],[[.,.],.]] [[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[5,2,3,1,6,7,4]=>[[[.,.],[.,.]],[[.,[.,.]],.]] [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[6,7,3,1,2,5,4]=>[[[.,[.,.]],.],[.,[[.,.],.]]] [[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[7,5,3,1,2,6,4]=>[[[[.,.],.],.],[.,[[.,.],.]]] [[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[6,5,3,1,2,7,4]=>[[[[.,.],.],.],[.,[[.,.],.]]] [[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[5,3,1,2,6,7,4]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[6,7,2,1,3,5,4]=>[[[.,[.,.]],.],[.,[[.,.],.]]] [[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[7,5,2,1,3,6,4]=>[[[[.,.],.],.],[.,[[.,.],.]]] [[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[6,5,2,1,3,7,4]=>[[[[.,.],.],.],[.,[[.,.],.]]] [[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[5,2,1,3,6,7,4]=>[[[.,.],.],[.,[[.,[.,.]],.]]] [[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[6,7,1,2,3,5,4]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[7,5,1,2,3,6,4]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[6,5,1,2,3,7,4]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[5,1,2,3,6,7,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],.],.],[.,.]] [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[6,4,3,2,1,7,5]=>[[[[[.,.],.],.],.],[[.,.],.]] [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[7,6,3,4,2,1,5]=>[[[[[.,.],.],[.,.]],.],[.,.]] [[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[6,3,4,2,1,7,5]=>[[[[.,.],[.,.]],.],[[.,.],.]] [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[7,6,4,2,3,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[6,4,2,3,1,7,5]=>[[[[.,.],.],[.,.]],[[.,.],.]] [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[7,6,3,2,4,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[6,3,2,4,1,7,5]=>[[[[.,.],.],[.,.]],[[.,.],.]] [[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[7,6,2,3,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[6,2,3,4,1,7,5]=>[[[.,.],[.,[.,.]]],[[.,.],.]] [[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[6,4,3,1,2,7,5]=>[[[[.,.],.],.],[.,[[.,.],.]]] [[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[7,6,3,1,4,2,5]=>[[[[.,.],.],.],[[.,.],[.,.]]] [[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[6,3,1,4,2,7,5]=>[[[.,.],.],[[.,.],[[.,.],.]]] [[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[6,4,2,1,3,7,5]=>[[[[.,.],.],.],[.,[[.,.],.]]] [[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[6,4,1,2,3,7,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[6,3,2,1,4,7,5]=>[[[[.,.],.],.],[.,[[.,.],.]]] [[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[7,6,2,3,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[6,2,3,1,4,7,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[6,3,1,2,4,7,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[6,2,1,3,4,7,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[6,1,2,3,4,7,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],.],[.,.]] [[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[7,4,5,3,2,1,6]=>[[[[[.,.],[.,.]],.],.],[.,.]] [[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[7,5,3,4,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]] [[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[7,4,3,5,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]] [[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[7,3,4,5,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[7,5,4,2,3,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[7,4,2,5,3,1,6]=>[[[[.,.],.],[[.,.],.]],[.,.]] [[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[7,5,3,2,4,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[7,5,2,3,4,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[7,4,3,2,5,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[7,3,4,2,5,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[7,4,2,3,5,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[7,3,2,4,5,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[7,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[7,4,5,1,3,2,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[7,5,3,1,4,2,6]=>[[[[.,.],.],.],[[.,.],[.,.]]] [[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[7,4,3,1,5,2,6]=>[[[[.,.],.],.],[[.,.],[.,.]]] [[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[7,3,1,4,5,2,6]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[7,5,4,2,1,3,6]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[7,4,2,1,5,3,6]=>[[[[.,.],.],.],[[.,.],[.,.]]] [[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[7,4,1,2,5,3,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[7,5,2,3,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[7,5,2,1,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[7,3,4,2,1,5,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[7,4,2,3,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[7,3,2,4,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[7,2,3,4,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[7,3,1,4,2,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[7,4,2,1,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[7,4,1,2,3,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[7,2,3,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[7,3,1,2,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[7,2,1,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]] [[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[5,6,4,3,2,1,7]=>[[[[[.,[.,.]],.],.],.],[.,.]] [[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[6,4,5,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]] [[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[5,4,6,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]] [[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[4,5,6,3,2,1,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[5,3,6,4,2,1,7]=>[[[[.,.],[[.,.],.]],.],[.,.]] [[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[6,4,3,5,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[6,3,4,5,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[4,5,3,6,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[5,3,4,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[4,3,5,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[3,4,5,6,2,1,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[6,5,4,2,3,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[5,6,2,4,3,1,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]] [[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[6,4,2,5,3,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]] [[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[5,4,2,6,3,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]] [[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[4,2,5,6,3,1,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]] [[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[6,5,3,2,4,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[5,3,2,6,4,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]] [[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[6,5,2,3,4,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[5,2,3,6,4,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[6,3,4,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[6,4,2,3,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[[.,[.,.]],.],[.,.]]],.]=>[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]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[4,5,3,2,6,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[5,3,4,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[4,3,5,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[3,4,5,2,6,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[5,4,2,3,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[4,2,5,3,6,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]] [[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[3,4,2,5,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[5,6,4,1,3,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[6,4,5,1,3,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[5,4,6,1,3,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[4,5,1,6,3,2,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[6,5,3,1,4,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[5,3,1,6,4,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]] [[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[6,4,3,1,5,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[6,3,1,4,5,2,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[5,4,3,1,6,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[4,5,1,3,6,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[5,3,1,4,6,2,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[4,3,1,5,6,2,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[3,1,4,5,6,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[6,5,4,2,1,3,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[5,6,2,1,4,3,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[6,4,2,1,5,3,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[5,4,2,1,6,3,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[4,2,1,5,6,3,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[5,6,1,2,4,3,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[6,4,1,2,5,3,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[5,4,1,2,6,3,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[4,1,2,5,6,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[5,3,2,1,6,4,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[6,5,2,3,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[5,2,3,1,6,4,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[5,3,1,2,6,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[6,5,2,1,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[5,2,1,3,6,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[5,1,2,3,6,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[6,3,4,2,1,5,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[6,4,2,3,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[6,3,2,4,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[6,3,1,4,2,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[6,4,2,1,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[6,4,1,2,3,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[6,3,1,2,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[.,[.,[.,[.,[.,.]]]]],.],.]=>[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]=>[5,3,4,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[[.,[.,[[.,[.,.]],.]]],.],.]=>[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]=>[5,4,2,3,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[4,2,5,3,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [[[.,[[.,[.,.]],[.,.]]],.],.]=>[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]=>[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]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[.,[[[.,[.,.]],.],.]],.],.]=>[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]=>[5,4,3,1,2,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[4,5,1,3,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[5,3,1,4,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[4,3,1,5,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[3,1,4,5,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[5,4,2,1,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[4,2,1,5,3,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[4,1,2,5,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[5,3,1,2,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[[.,[.,[.,[.,.]]]],.],.],.]=>[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]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[[.,[[.,[.,.]],.]],.],.],.]=>[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]=>[4,3,1,2,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[3,1,4,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[[[.,[.,[.,.]]],.],.],.],.]=>[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]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[[[[.,[.,.]],.],.],.],.],.]=>[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]=>[[[[[[[[.,.],.],.],.],.],.],.],.] [[[[[[[[.,.],.],.],.],.],.],.],.]=>[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
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
  • $1$
  • $|1|4 \to 14$
  • $|14|2 \to 412$
  • $|4|1|2|5 \to 4125$
  • $|4|125|3 \to 45123.$
In total, this gives $\phi([1,4,2,5,3]) = [4,5,1,2,3]$.
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
Map
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.