Identifier
Values
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>0 [.,[.,.]]=>[2,1]=>1 [[.,.],.]=>[1,2]=>0 [.,[.,[.,.]]]=>[3,2,1]=>3 [.,[[.,.],.]]=>[2,3,1]=>2 [[.,.],[.,.]]=>[1,3,2]=>1 [[.,[.,.]],.]=>[2,1,3]=>1 [[[.,.],.],.]=>[1,2,3]=>0 [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>6 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>5 [.,[[.,.],[.,.]]]=>[2,4,3,1]=>4 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>4 [.,[[[.,.],.],.]]=>[2,3,4,1]=>3 [[.,.],[.,[.,.]]]=>[1,4,3,2]=>3 [[.,.],[[.,.],.]]=>[1,3,4,2]=>2 [[.,[.,.]],[.,.]]=>[2,1,4,3]=>2 [[[.,.],.],[.,.]]=>[1,2,4,3]=>1 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>3 [[.,[[.,.],.]],.]=>[2,3,1,4]=>2 [[[.,.],[.,.]],.]=>[1,3,2,4]=>1 [[[.,[.,.]],.],.]=>[2,1,3,4]=>1 [[[[.,.],.],.],.]=>[1,2,3,4]=>0 [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>10 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>9 [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>8 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>8 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>7 [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>7 [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>6 [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>6 [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>5 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>7 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>6 [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>5 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>5 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>4 [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>6 [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>5 [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>4 [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>4 [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>3 [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>4 [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>3 [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>3 [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>2 [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>4 [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>3 [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>2 [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>2 [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>1 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>6 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>5 [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>4 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>4 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>3 [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>3 [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>2 [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>2 [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>1 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>3 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>2 [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>1 [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>1 [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>0 [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>15 [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>14 [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>13 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>13 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>12 [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>12 [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>11 [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>11 [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>10 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>12 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>11 [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>10 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>10 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>9 [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>11 [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>10 [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>9 [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>9 [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>8 [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>9 [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>8 [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>8 [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>7 [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>9 [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>8 [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>7 [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>7 [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>6 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>11 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>10 [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>9 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>9 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>8 [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>8 [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>7 [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>7 [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>6 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>8 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>7 [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>6 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>6 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>5 [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>10 [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>9 [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>8 [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>8 [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>7 [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>7 [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>6 [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>6 [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>5 [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>7 [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>6 [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>5 [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>5 [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>4 [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>7 [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>6 [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>5 [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>5 [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>4 [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>6 [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>5 [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>4 [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>4 [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>3 [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>6 [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>5 [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>5 [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>4 [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>4 [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>3 [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>4 [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>3 [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>3 [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>2 [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>7 [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>6 [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>5 [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>5 [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>4 [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>4 [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>3 [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>3 [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>2 [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>4 [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>3 [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>2 [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>2 [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>1 [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>10 [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>9 [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>8 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>8 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>7 [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>7 [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>6 [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>6 [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>5 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>7 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>6 [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>5 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>5 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>4 [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>6 [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>5 [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>4 [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>4 [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>3 [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>4 [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>3 [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>3 [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>2 [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>4 [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>3 [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>2 [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>2 [[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>1 [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>6 [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>5 [[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>4 [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>4 [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>3 [[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>3 [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>2 [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>2 [[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>1 [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>3 [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>2 [[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>1 [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>1 [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>0 [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>21 [.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>10 [.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>10 [.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>9 [.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>9 [.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>8 [.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>7 [.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>6 [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>15 [[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>14 [[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>13 [[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>13 [[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>12 [[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>12 [[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>11 [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>11 [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>12 [[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>11 [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>11 [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>11 [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>11 [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>11 [[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>5 [[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>4 [[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>1 [[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>15 [[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>14 [[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>13 [[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>13 [[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>12 [[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>12 [[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>11 [[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>11 [[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>12 [[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>11 [[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>11 [[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>11 [[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>5 [[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>1 [[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>10 [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>4 [[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>6 [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>3 [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>3 [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>2 [[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>1 [[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>1 [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>0 [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>28 [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>26 [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>24 [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>24 [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>22 [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>20 [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>16 [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>20 [.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>12 [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[3,2,6,5,4,8,7,1]=>12 [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>22 [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>20 [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>18 [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>16 [.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>14 [.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>12 [.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>12 [.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>10 [.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>10 [.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>10 [.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>9 [.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>8 [.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>7 [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>21 [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>20 [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>19 [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>19 [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>18 [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>18 [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>18 [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>12 [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>13 [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>13 [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>9 [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>16 [[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>10 [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>8 [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>12 [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>13 [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>9 [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>4 [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>12 [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>10 [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>8 [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>8 [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>8 [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>8 [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>6 [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>8 [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>6 [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>6 [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>13 [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>9 [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>6 [[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>4 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>16 [[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>10 [[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>8 [[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>6 [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>8 [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>6 [[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>6 [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>8 [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>6 [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>6 [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>4 [[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>2 [[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>1 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>21 [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>20 [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>19 [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>19 [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>18 [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>18 [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>18 [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>13 [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>13 [[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>9 [[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>6 [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>6 [[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>4 [[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>3 [[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>2 [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>2 [[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>1 [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>15 [[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>5 [[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>2 [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>10 [[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>4 [[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>2 [[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>1 [[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>6 [[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>3 [[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>1 [[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>1 [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>0 [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>36 [.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>8 [[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>0 [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>45 [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>9 [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>0 [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>28 [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>36 [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]=>5 [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>6 [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]=>1 [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]=>1 [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>9 [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]=>1 [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>10 [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>10 [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>10 [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]=>28 [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>27 [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,8,9,7,6,5,4,3,2]=>27 [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]=>36 [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>45 [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>35 [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>26 [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,8,7,9,6,5,4,3,2]=>26 [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[1,9,10,8,7,6,5,4,3,2]=>35 [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]=>45 [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]=>29 [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]=>21 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[6,5,4,3,2,1,10,9,8,7]=>21 [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[8,7,6,5,4,3,2,1,10,9]=>29 [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>21 [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>15 [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>10 [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>6 [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>3 [[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>1 [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>28 [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>21 [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>15 [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>10 [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>6 [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>3 [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>1 [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>1 [[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>7 [[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>6 [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>8
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Description
The number of inversions of a permutation.
This equals the minimal number of simple transpositions $(i,i+1)$ needed to write $\pi$. Thus, it is also the Coxeter length of $\pi$.
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.