Identifier
-
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
St000245: Permutations ⟶ ℤ
Values
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>0
[.,[.,.]]=>[2,1]=>0
[[.,.],.]=>[1,2]=>1
[.,[.,[.,.]]]=>[3,2,1]=>0
[.,[[.,.],.]]=>[2,3,1]=>1
[[.,.],[.,.]]=>[3,1,2]=>1
[[.,[.,.]],.]=>[2,1,3]=>1
[[[.,.],.],.]=>[1,2,3]=>2
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>0
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>1
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>1
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>1
[.,[[[.,.],.],.]]=>[2,3,4,1]=>2
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>1
[[.,.],[[.,.],.]]=>[3,4,1,2]=>2
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>1
[[[.,.],.],[.,.]]=>[4,1,2,3]=>2
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>1
[[.,[[.,.],.]],.]=>[2,3,1,4]=>2
[[[.,.],[.,.]],.]=>[3,1,2,4]=>2
[[[.,[.,.]],.],.]=>[2,1,3,4]=>2
[[[[.,.],.],.],.]=>[1,2,3,4]=>3
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>0
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>1
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>1
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>1
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>2
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>1
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>2
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>1
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>2
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>1
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>2
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>2
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>2
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>3
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>1
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>2
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>2
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>2
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>3
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>1
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>2
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>2
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>3
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>1
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>2
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>2
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>2
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>3
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>1
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>2
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>2
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>2
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>3
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>2
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>3
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>2
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>3
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>2
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>3
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>3
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>3
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>4
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>0
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>1
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>1
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>1
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>2
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>1
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>2
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>1
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>2
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>1
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>2
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>2
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>2
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>3
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>1
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>2
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>2
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>2
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>3
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>1
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>2
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>2
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>3
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>1
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>2
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>2
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>2
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>3
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>1
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>2
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>2
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>2
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>3
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>2
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>3
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>2
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>3
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>2
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>3
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>3
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>3
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>4
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>1
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>2
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>2
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>2
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>3
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>2
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>3
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>2
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>3
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>2
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>3
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>3
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>3
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>4
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>1
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>2
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>2
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>3
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>2
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>3
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>3
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>3
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>4
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>1
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>2
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>2
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>3
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>3
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>2
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>3
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>3
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>4
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>1
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>2
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>2
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>2
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>3
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>2
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>3
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>2
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>3
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>2
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>3
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>3
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>3
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>4
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>1
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>2
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>2
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>2
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>3
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>2
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>3
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>2
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>3
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>2
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>3
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>3
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>3
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>4
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>2
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>3
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>3
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>3
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>4
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>2
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>3
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>3
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>4
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>2
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>3
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>3
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>3
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>4
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>2
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>3
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>3
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>3
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>4
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>3
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>4
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>3
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>4
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>3
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>4
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>4
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>4
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>5
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>0
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>4
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>4
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>3
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>4
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>4
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>3
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>4
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>3
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>4
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>4
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>4
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>5
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>1
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>2
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>3
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>5
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>2
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>4
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>4
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>4
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>4
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>4
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>5
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>4
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>4
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>5
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>4
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>4
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>3
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>4
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>4
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>3
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>4
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>3
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>4
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>4
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>4
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>5
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>1
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>2
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>2
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>3
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>2
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>2
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>3
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>2
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>3
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>2
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>3
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>2
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>5
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>4
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>5
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>5
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>5
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>2
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>5
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>5
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>3
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>5
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>5
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>5
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>4
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>5
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>5
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>5
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>6
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>0
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>1
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>2
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>2
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>2
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>1
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>2
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>2
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>2
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>2
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>4
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>2
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>2
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>2
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>2
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>2
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>4
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>4
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>4
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>1
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>2
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>2
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>3
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>5
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>5
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>4
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>5
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>5
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>5
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>6
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>1
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>2
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>2
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>2
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>2
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>2
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>3
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>4
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>5
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>5
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>6
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>1
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>2
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>2
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>4
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>4
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>3
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>4
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>4
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>5
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>5
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>2
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>4
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>4
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>4
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>3
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>4
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>5
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>5
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>6
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>1
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>2
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>4
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>5
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>6
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>3
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>4
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>5
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>6
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>1
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>2
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>4
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>2
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>2
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>3
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>5
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>5
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>4
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>5
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>5
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>5
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>6
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>1
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>2
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>2
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>3
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>2
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>2
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>3
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>2
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>3
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>2
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>3
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>3
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>5
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>6
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>6
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>6
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>6
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>2
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>6
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>5
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>6
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>6
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>3
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>6
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>6
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>4
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>6
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>5
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>6
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>7
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>0
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>7
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>8
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>0
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>8
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>9
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>1
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>1
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>5
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>7
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>8
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>6
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>6
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>9
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>7
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>6
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>6
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[4,2,3,5,6,7,8,9,1]=>6
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>6
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>7
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>9
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>7
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>7
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>7
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>6
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>8
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>8
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>8
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>8
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>1
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>2
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>1
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>1
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>2
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>2
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>2
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>2
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>3
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>4
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>5
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>6
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>7
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>2
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>3
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>4
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>5
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>6
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>7
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>8
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>9
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>7
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>7
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>8
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>7
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>7
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>8
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>2
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>7
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>5
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>4
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>3
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>6
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>5
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>4
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>3
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>7
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Description
The number of ascents of a permutation.
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to 132-avoiding permutation
Description
Return a 132-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 maximal element of the Sylvester class.
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 maximal element of the Sylvester class.
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