edit this statistic or download as text // json
Identifier
Values
=>
[1,2]=>1 [2,1]=>1 [1,2,3]=>1 [1,3,2]=>2 [2,1,3]=>2 [2,3,1]=>2 [3,1,2]=>2 [3,2,1]=>1 [1,2,3,4]=>1 [1,2,4,3]=>3 [1,3,2,4]=>5 [1,3,4,2]=>3 [1,4,2,3]=>5 [1,4,3,2]=>3 [2,1,3,4]=>3 [2,1,4,3]=>5 [2,3,1,4]=>5 [2,3,4,1]=>3 [2,4,1,3]=>5 [2,4,3,1]=>3 [3,1,2,4]=>3 [3,1,4,2]=>5 [3,2,1,4]=>3 [3,2,4,1]=>5 [3,4,1,2]=>5 [3,4,2,1]=>3 [4,1,2,3]=>3 [4,1,3,2]=>5 [4,2,1,3]=>3 [4,2,3,1]=>5 [4,3,1,2]=>3 [4,3,2,1]=>1 [1,2,3,4,5]=>1 [1,2,3,5,4]=>4 [1,2,4,3,5]=>9 [1,2,4,5,3]=>4 [1,2,5,3,4]=>9 [1,2,5,4,3]=>6 [1,3,2,4,5]=>9 [1,3,2,5,4]=>16 [1,3,4,2,5]=>9 [1,3,4,5,2]=>4 [1,3,5,2,4]=>9 [1,3,5,4,2]=>6 [1,4,2,3,5]=>9 [1,4,2,5,3]=>16 [1,4,3,2,5]=>11 [1,4,3,5,2]=>16 [1,4,5,2,3]=>9 [1,4,5,3,2]=>6 [1,5,2,3,4]=>9 [1,5,2,4,3]=>16 [1,5,3,2,4]=>11 [1,5,3,4,2]=>16 [1,5,4,2,3]=>11 [1,5,4,3,2]=>4 [2,1,3,4,5]=>4 [2,1,3,5,4]=>11 [2,1,4,3,5]=>16 [2,1,4,5,3]=>11 [2,1,5,3,4]=>16 [2,1,5,4,3]=>9 [2,3,1,4,5]=>9 [2,3,1,5,4]=>16 [2,3,4,1,5]=>9 [2,3,4,5,1]=>4 [2,3,5,1,4]=>9 [2,3,5,4,1]=>6 [2,4,1,3,5]=>9 [2,4,1,5,3]=>16 [2,4,3,1,5]=>11 [2,4,3,5,1]=>16 [2,4,5,1,3]=>9 [2,4,5,3,1]=>6 [2,5,1,3,4]=>9 [2,5,1,4,3]=>16 [2,5,3,1,4]=>11 [2,5,3,4,1]=>16 [2,5,4,1,3]=>11 [2,5,4,3,1]=>4 [3,1,2,4,5]=>4 [3,1,2,5,4]=>11 [3,1,4,2,5]=>16 [3,1,4,5,2]=>11 [3,1,5,2,4]=>16 [3,1,5,4,2]=>9 [3,2,1,4,5]=>6 [3,2,1,5,4]=>9 [3,2,4,1,5]=>16 [3,2,4,5,1]=>11 [3,2,5,1,4]=>16 [3,2,5,4,1]=>9 [3,4,1,2,5]=>9 [3,4,1,5,2]=>16 [3,4,2,1,5]=>11 [3,4,2,5,1]=>16 [3,4,5,1,2]=>9 [3,4,5,2,1]=>6 [3,5,1,2,4]=>9 [3,5,1,4,2]=>16 [3,5,2,1,4]=>11 [3,5,2,4,1]=>16 [3,5,4,1,2]=>11 [3,5,4,2,1]=>4 [4,1,2,3,5]=>4 [4,1,2,5,3]=>11 [4,1,3,2,5]=>16 [4,1,3,5,2]=>11 [4,1,5,2,3]=>16 [4,1,5,3,2]=>9 [4,2,1,3,5]=>6 [4,2,1,5,3]=>9 [4,2,3,1,5]=>16 [4,2,3,5,1]=>11 [4,2,5,1,3]=>16 [4,2,5,3,1]=>9 [4,3,1,2,5]=>6 [4,3,1,5,2]=>9 [4,3,2,1,5]=>4 [4,3,2,5,1]=>9 [4,3,5,1,2]=>16 [4,3,5,2,1]=>9 [4,5,1,2,3]=>9 [4,5,1,3,2]=>16 [4,5,2,1,3]=>11 [4,5,2,3,1]=>16 [4,5,3,1,2]=>11 [4,5,3,2,1]=>4 [5,1,2,3,4]=>4 [5,1,2,4,3]=>11 [5,1,3,2,4]=>16 [5,1,3,4,2]=>11 [5,1,4,2,3]=>16 [5,1,4,3,2]=>9 [5,2,1,3,4]=>6 [5,2,1,4,3]=>9 [5,2,3,1,4]=>16 [5,2,3,4,1]=>11 [5,2,4,1,3]=>16 [5,2,4,3,1]=>9 [5,3,1,2,4]=>6 [5,3,1,4,2]=>9 [5,3,2,1,4]=>4 [5,3,2,4,1]=>9 [5,3,4,1,2]=>16 [5,3,4,2,1]=>9 [5,4,1,2,3]=>6 [5,4,1,3,2]=>9 [5,4,2,1,3]=>4 [5,4,2,3,1]=>9 [5,4,3,1,2]=>4 [5,4,3,2,1]=>1 [1,2,3,4,5,6]=>1 [1,2,3,4,6,5]=>5 [1,2,3,5,4,6]=>14 [1,2,3,5,6,4]=>5 [1,2,3,6,4,5]=>14 [1,2,3,6,5,4]=>10 [1,2,4,3,5,6]=>19 [1,2,4,3,6,5]=>35 [1,2,4,5,3,6]=>14 [1,2,4,5,6,3]=>5 [1,2,4,6,3,5]=>14 [1,2,4,6,5,3]=>10 [1,2,5,3,4,6]=>19 [1,2,5,3,6,4]=>35 [1,2,5,4,3,6]=>26 [1,2,5,4,6,3]=>35 [1,2,5,6,3,4]=>14 [1,2,5,6,4,3]=>10 [1,2,6,3,4,5]=>19 [1,2,6,3,5,4]=>35 [1,2,6,4,3,5]=>26 [1,2,6,4,5,3]=>35 [1,2,6,5,3,4]=>26 [1,2,6,5,4,3]=>10 [1,3,2,4,5,6]=>14 [1,3,2,4,6,5]=>40 [1,3,2,5,4,6]=>61 [1,3,2,5,6,4]=>40 [1,3,2,6,4,5]=>61 [1,3,2,6,5,4]=>35 [1,3,4,2,5,6]=>19 [1,3,4,2,6,5]=>35 [1,3,4,5,2,6]=>14 [1,3,4,5,6,2]=>5 [1,3,4,6,2,5]=>14 [1,3,4,6,5,2]=>10 [1,3,5,2,4,6]=>19 [1,3,5,2,6,4]=>35 [1,3,5,4,2,6]=>26 [1,3,5,4,6,2]=>35 [1,3,5,6,2,4]=>14 [1,3,5,6,4,2]=>10 [1,3,6,2,4,5]=>19 [1,3,6,2,5,4]=>35 [1,3,6,4,2,5]=>26 [1,3,6,4,5,2]=>35 [1,3,6,5,2,4]=>26 [1,3,6,5,4,2]=>10 [1,4,2,3,5,6]=>14 [1,4,2,3,6,5]=>40 [1,4,2,5,3,6]=>61 [1,4,2,5,6,3]=>40 [1,4,2,6,3,5]=>61 [1,4,2,6,5,3]=>35 [1,4,3,2,5,6]=>26 [1,4,3,2,6,5]=>40 [1,4,3,5,2,6]=>61 [1,4,3,5,6,2]=>40 [1,4,3,6,2,5]=>61 [1,4,3,6,5,2]=>35 [1,4,5,2,3,6]=>19 [1,4,5,2,6,3]=>35 [1,4,5,3,2,6]=>26 [1,4,5,3,6,2]=>35 [1,4,5,6,2,3]=>14 [1,4,5,6,3,2]=>10 [1,4,6,2,3,5]=>19 [1,4,6,2,5,3]=>35 [1,4,6,3,2,5]=>26 [1,4,6,3,5,2]=>35 [1,4,6,5,2,3]=>26 [1,4,6,5,3,2]=>10 [1,5,2,3,4,6]=>14 [1,5,2,3,6,4]=>40 [1,5,2,4,3,6]=>61 [1,5,2,4,6,3]=>40 [1,5,2,6,3,4]=>61 [1,5,2,6,4,3]=>35 [1,5,3,2,4,6]=>26 [1,5,3,2,6,4]=>40 [1,5,3,4,2,6]=>61 [1,5,3,4,6,2]=>40 [1,5,3,6,2,4]=>61 [1,5,3,6,4,2]=>35 [1,5,4,2,3,6]=>26 [1,5,4,2,6,3]=>40 [1,5,4,3,2,6]=>19 [1,5,4,3,6,2]=>40 [1,5,4,6,2,3]=>61 [1,5,4,6,3,2]=>35 [1,5,6,2,3,4]=>19 [1,5,6,2,4,3]=>35 [1,5,6,3,2,4]=>26 [1,5,6,3,4,2]=>35 [1,5,6,4,2,3]=>26 [1,5,6,4,3,2]=>10 [1,6,2,3,4,5]=>14 [1,6,2,3,5,4]=>40 [1,6,2,4,3,5]=>61 [1,6,2,4,5,3]=>40 [1,6,2,5,3,4]=>61 [1,6,2,5,4,3]=>35 [1,6,3,2,4,5]=>26 [1,6,3,2,5,4]=>40 [1,6,3,4,2,5]=>61 [1,6,3,4,5,2]=>40 [1,6,3,5,2,4]=>61 [1,6,3,5,4,2]=>35 [1,6,4,2,3,5]=>26 [1,6,4,2,5,3]=>40 [1,6,4,3,2,5]=>19 [1,6,4,3,5,2]=>40 [1,6,4,5,2,3]=>61 [1,6,4,5,3,2]=>35 [1,6,5,2,3,4]=>26 [1,6,5,2,4,3]=>40 [1,6,5,3,2,4]=>19 [1,6,5,3,4,2]=>40 [1,6,5,4,2,3]=>19 [1,6,5,4,3,2]=>5 [2,1,3,4,5,6]=>5 [2,1,3,4,6,5]=>19 [2,1,3,5,4,6]=>40 [2,1,3,5,6,4]=>19 [2,1,3,6,4,5]=>40 [2,1,3,6,5,4]=>26 [2,1,4,3,5,6]=>35 [2,1,4,3,6,5]=>61 [2,1,4,5,3,6]=>40 [2,1,4,5,6,3]=>19 [2,1,4,6,3,5]=>40 [2,1,4,6,5,3]=>26 [2,1,5,3,4,6]=>35 [2,1,5,3,6,4]=>61 [2,1,5,4,3,6]=>40 [2,1,5,4,6,3]=>61 [2,1,5,6,3,4]=>40 [2,1,5,6,4,3]=>26 [2,1,6,3,4,5]=>35 [2,1,6,3,5,4]=>61 [2,1,6,4,3,5]=>40 [2,1,6,4,5,3]=>61 [2,1,6,5,3,4]=>40 [2,1,6,5,4,3]=>14 [2,3,1,4,5,6]=>14 [2,3,1,4,6,5]=>40 [2,3,1,5,4,6]=>61 [2,3,1,5,6,4]=>40 [2,3,1,6,4,5]=>61 [2,3,1,6,5,4]=>35 [2,3,4,1,5,6]=>19 [2,3,4,1,6,5]=>35 [2,3,4,5,1,6]=>14 [2,3,4,5,6,1]=>5 [2,3,4,6,1,5]=>14 [2,3,4,6,5,1]=>10 [2,3,5,1,4,6]=>19 [2,3,5,1,6,4]=>35 [2,3,5,4,1,6]=>26 [2,3,5,4,6,1]=>35 [2,3,5,6,1,4]=>14 [2,3,5,6,4,1]=>10 [2,3,6,1,4,5]=>19 [2,3,6,1,5,4]=>35 [2,3,6,4,1,5]=>26 [2,3,6,4,5,1]=>35 [2,3,6,5,1,4]=>26 [2,3,6,5,4,1]=>10 [2,4,1,3,5,6]=>14 [2,4,1,3,6,5]=>40 [2,4,1,5,3,6]=>61 [2,4,1,5,6,3]=>40 [2,4,1,6,3,5]=>61 [2,4,1,6,5,3]=>35 [2,4,3,1,5,6]=>26 [2,4,3,1,6,5]=>40 [2,4,3,5,1,6]=>61 [2,4,3,5,6,1]=>40 [2,4,3,6,1,5]=>61 [2,4,3,6,5,1]=>35 [2,4,5,1,3,6]=>19 [2,4,5,1,6,3]=>35 [2,4,5,3,1,6]=>26 [2,4,5,3,6,1]=>35 [2,4,5,6,1,3]=>14 [2,4,5,6,3,1]=>10 [2,4,6,1,3,5]=>19 [2,4,6,1,5,3]=>35 [2,4,6,3,1,5]=>26 [2,4,6,3,5,1]=>35 [2,4,6,5,1,3]=>26 [2,4,6,5,3,1]=>10 [2,5,1,3,4,6]=>14 [2,5,1,3,6,4]=>40 [2,5,1,4,3,6]=>61 [2,5,1,4,6,3]=>40 [2,5,1,6,3,4]=>61 [2,5,1,6,4,3]=>35 [2,5,3,1,4,6]=>26 [2,5,3,1,6,4]=>40 [2,5,3,4,1,6]=>61 [2,5,3,4,6,1]=>40 [2,5,3,6,1,4]=>61 [2,5,3,6,4,1]=>35 [2,5,4,1,3,6]=>26 [2,5,4,1,6,3]=>40 [2,5,4,3,1,6]=>19 [2,5,4,3,6,1]=>40 [2,5,4,6,1,3]=>61 [2,5,4,6,3,1]=>35 [2,5,6,1,3,4]=>19 [2,5,6,1,4,3]=>35 [2,5,6,3,1,4]=>26 [2,5,6,3,4,1]=>35 [2,5,6,4,1,3]=>26 [2,5,6,4,3,1]=>10 [2,6,1,3,4,5]=>14 [2,6,1,3,5,4]=>40 [2,6,1,4,3,5]=>61 [2,6,1,4,5,3]=>40 [2,6,1,5,3,4]=>61 [2,6,1,5,4,3]=>35 [2,6,3,1,4,5]=>26 [2,6,3,1,5,4]=>40 [2,6,3,4,1,5]=>61 [2,6,3,4,5,1]=>40 [2,6,3,5,1,4]=>61 [2,6,3,5,4,1]=>35 [2,6,4,1,3,5]=>26 [2,6,4,1,5,3]=>40 [2,6,4,3,1,5]=>19 [2,6,4,3,5,1]=>40 [2,6,4,5,1,3]=>61 [2,6,4,5,3,1]=>35 [2,6,5,1,3,4]=>26 [2,6,5,1,4,3]=>40 [2,6,5,3,1,4]=>19 [2,6,5,3,4,1]=>40 [2,6,5,4,1,3]=>19 [2,6,5,4,3,1]=>5 [3,1,2,4,5,6]=>5 [3,1,2,4,6,5]=>19 [3,1,2,5,4,6]=>40 [3,1,2,5,6,4]=>19 [3,1,2,6,4,5]=>40 [3,1,2,6,5,4]=>26 [3,1,4,2,5,6]=>35 [3,1,4,2,6,5]=>61 [3,1,4,5,2,6]=>40 [3,1,4,5,6,2]=>19 [3,1,4,6,2,5]=>40 [3,1,4,6,5,2]=>26 [3,1,5,2,4,6]=>35 [3,1,5,2,6,4]=>61 [3,1,5,4,2,6]=>40 [3,1,5,4,6,2]=>61 [3,1,5,6,2,4]=>40 [3,1,5,6,4,2]=>26 [3,1,6,2,4,5]=>35 [3,1,6,2,5,4]=>61 [3,1,6,4,2,5]=>40 [3,1,6,4,5,2]=>61 [3,1,6,5,2,4]=>40 [3,1,6,5,4,2]=>14 [3,2,1,4,5,6]=>10 [3,2,1,4,6,5]=>26 [3,2,1,5,4,6]=>35 [3,2,1,5,6,4]=>26 [3,2,1,6,4,5]=>35 [3,2,1,6,5,4]=>19 [3,2,4,1,5,6]=>35 [3,2,4,1,6,5]=>61 [3,2,4,5,1,6]=>40 [3,2,4,5,6,1]=>19 [3,2,4,6,1,5]=>40 [3,2,4,6,5,1]=>26 [3,2,5,1,4,6]=>35 [3,2,5,1,6,4]=>61 [3,2,5,4,1,6]=>40 [3,2,5,4,6,1]=>61 [3,2,5,6,1,4]=>40 [3,2,5,6,4,1]=>26 [3,2,6,1,4,5]=>35 [3,2,6,1,5,4]=>61 [3,2,6,4,1,5]=>40 [3,2,6,4,5,1]=>61 [3,2,6,5,1,4]=>40 [3,2,6,5,4,1]=>14 [3,4,1,2,5,6]=>14 [3,4,1,2,6,5]=>40 [3,4,1,5,2,6]=>61 [3,4,1,5,6,2]=>40 [3,4,1,6,2,5]=>61 [3,4,1,6,5,2]=>35 [3,4,2,1,5,6]=>26 [3,4,2,1,6,5]=>40 [3,4,2,5,1,6]=>61 [3,4,2,5,6,1]=>40 [3,4,2,6,1,5]=>61 [3,4,2,6,5,1]=>35 [3,4,5,1,2,6]=>19 [3,4,5,1,6,2]=>35 [3,4,5,2,1,6]=>26 [3,4,5,2,6,1]=>35 [3,4,5,6,1,2]=>14 [3,4,5,6,2,1]=>10 [3,4,6,1,2,5]=>19 [3,4,6,1,5,2]=>35 [3,4,6,2,1,5]=>26 [3,4,6,2,5,1]=>35 [3,4,6,5,1,2]=>26 [3,4,6,5,2,1]=>10 [3,5,1,2,4,6]=>14 [3,5,1,2,6,4]=>40 [3,5,1,4,2,6]=>61 [3,5,1,4,6,2]=>40 [3,5,1,6,2,4]=>61 [3,5,1,6,4,2]=>35 [3,5,2,1,4,6]=>26 [3,5,2,1,6,4]=>40 [3,5,2,4,1,6]=>61 [3,5,2,4,6,1]=>40 [3,5,2,6,1,4]=>61 [3,5,2,6,4,1]=>35 [3,5,4,1,2,6]=>26 [3,5,4,1,6,2]=>40 [3,5,4,2,1,6]=>19 [3,5,4,2,6,1]=>40 [3,5,4,6,1,2]=>61 [3,5,4,6,2,1]=>35 [3,5,6,1,2,4]=>19 [3,5,6,1,4,2]=>35 [3,5,6,2,1,4]=>26 [3,5,6,2,4,1]=>35 [3,5,6,4,1,2]=>26 [3,5,6,4,2,1]=>10 [3,6,1,2,4,5]=>14 [3,6,1,2,5,4]=>40 [3,6,1,4,2,5]=>61 [3,6,1,4,5,2]=>40 [3,6,1,5,2,4]=>61 [3,6,1,5,4,2]=>35 [3,6,2,1,4,5]=>26 [3,6,2,1,5,4]=>40 [3,6,2,4,1,5]=>61 [3,6,2,4,5,1]=>40 [3,6,2,5,1,4]=>61 [3,6,2,5,4,1]=>35 [3,6,4,1,2,5]=>26 [3,6,4,1,5,2]=>40 [3,6,4,2,1,5]=>19 [3,6,4,2,5,1]=>40 [3,6,4,5,1,2]=>61 [3,6,4,5,2,1]=>35 [3,6,5,1,2,4]=>26 [3,6,5,1,4,2]=>40 [3,6,5,2,1,4]=>19 [3,6,5,2,4,1]=>40 [3,6,5,4,1,2]=>19 [3,6,5,4,2,1]=>5 [4,1,2,3,5,6]=>5 [4,1,2,3,6,5]=>19 [4,1,2,5,3,6]=>40 [4,1,2,5,6,3]=>19 [4,1,2,6,3,5]=>40 [4,1,2,6,5,3]=>26 [4,1,3,2,5,6]=>35 [4,1,3,2,6,5]=>61 [4,1,3,5,2,6]=>40 [4,1,3,5,6,2]=>19 [4,1,3,6,2,5]=>40 [4,1,3,6,5,2]=>26 [4,1,5,2,3,6]=>35 [4,1,5,2,6,3]=>61 [4,1,5,3,2,6]=>40 [4,1,5,3,6,2]=>61 [4,1,5,6,2,3]=>40 [4,1,5,6,3,2]=>26 [4,1,6,2,3,5]=>35 [4,1,6,2,5,3]=>61 [4,1,6,3,2,5]=>40 [4,1,6,3,5,2]=>61 [4,1,6,5,2,3]=>40 [4,1,6,5,3,2]=>14 [4,2,1,3,5,6]=>10 [4,2,1,3,6,5]=>26 [4,2,1,5,3,6]=>35 [4,2,1,5,6,3]=>26 [4,2,1,6,3,5]=>35 [4,2,1,6,5,3]=>19 [4,2,3,1,5,6]=>35 [4,2,3,1,6,5]=>61 [4,2,3,5,1,6]=>40 [4,2,3,5,6,1]=>19 [4,2,3,6,1,5]=>40 [4,2,3,6,5,1]=>26 [4,2,5,1,3,6]=>35 [4,2,5,1,6,3]=>61 [4,2,5,3,1,6]=>40 [4,2,5,3,6,1]=>61 [4,2,5,6,1,3]=>40 [4,2,5,6,3,1]=>26 [4,2,6,1,3,5]=>35 [4,2,6,1,5,3]=>61 [4,2,6,3,1,5]=>40 [4,2,6,3,5,1]=>61 [4,2,6,5,1,3]=>40 [4,2,6,5,3,1]=>14 [4,3,1,2,5,6]=>10 [4,3,1,2,6,5]=>26 [4,3,1,5,2,6]=>35 [4,3,1,5,6,2]=>26 [4,3,1,6,2,5]=>35 [4,3,1,6,5,2]=>19 [4,3,2,1,5,6]=>10 [4,3,2,1,6,5]=>14 [4,3,2,5,1,6]=>35 [4,3,2,5,6,1]=>26 [4,3,2,6,1,5]=>35 [4,3,2,6,5,1]=>19 [4,3,5,1,2,6]=>35 [4,3,5,1,6,2]=>61 [4,3,5,2,1,6]=>40 [4,3,5,2,6,1]=>61 [4,3,5,6,1,2]=>40 [4,3,5,6,2,1]=>26 [4,3,6,1,2,5]=>35 [4,3,6,1,5,2]=>61 [4,3,6,2,1,5]=>40 [4,3,6,2,5,1]=>61 [4,3,6,5,1,2]=>40 [4,3,6,5,2,1]=>14 [4,5,1,2,3,6]=>14 [4,5,1,2,6,3]=>40 [4,5,1,3,2,6]=>61 [4,5,1,3,6,2]=>40 [4,5,1,6,2,3]=>61 [4,5,1,6,3,2]=>35 [4,5,2,1,3,6]=>26 [4,5,2,1,6,3]=>40 [4,5,2,3,1,6]=>61 [4,5,2,3,6,1]=>40 [4,5,2,6,1,3]=>61 [4,5,2,6,3,1]=>35 [4,5,3,1,2,6]=>26 [4,5,3,1,6,2]=>40 [4,5,3,2,1,6]=>19 [4,5,3,2,6,1]=>40 [4,5,3,6,1,2]=>61 [4,5,3,6,2,1]=>35 [4,5,6,1,2,3]=>19 [4,5,6,1,3,2]=>35 [4,5,6,2,1,3]=>26 [4,5,6,2,3,1]=>35 [4,5,6,3,1,2]=>26 [4,5,6,3,2,1]=>10 [4,6,1,2,3,5]=>14 [4,6,1,2,5,3]=>40 [4,6,1,3,2,5]=>61 [4,6,1,3,5,2]=>40 [4,6,1,5,2,3]=>61 [4,6,1,5,3,2]=>35 [4,6,2,1,3,5]=>26 [4,6,2,1,5,3]=>40 [4,6,2,3,1,5]=>61 [4,6,2,3,5,1]=>40 [4,6,2,5,1,3]=>61 [4,6,2,5,3,1]=>35 [4,6,3,1,2,5]=>26 [4,6,3,1,5,2]=>40 [4,6,3,2,1,5]=>19 [4,6,3,2,5,1]=>40 [4,6,3,5,1,2]=>61 [4,6,3,5,2,1]=>35 [4,6,5,1,2,3]=>26 [4,6,5,1,3,2]=>40 [4,6,5,2,1,3]=>19 [4,6,5,2,3,1]=>40 [4,6,5,3,1,2]=>19 [4,6,5,3,2,1]=>5 [5,1,2,3,4,6]=>5 [5,1,2,3,6,4]=>19 [5,1,2,4,3,6]=>40 [5,1,2,4,6,3]=>19 [5,1,2,6,3,4]=>40 [5,1,2,6,4,3]=>26 [5,1,3,2,4,6]=>35 [5,1,3,2,6,4]=>61 [5,1,3,4,2,6]=>40 [5,1,3,4,6,2]=>19 [5,1,3,6,2,4]=>40 [5,1,3,6,4,2]=>26 [5,1,4,2,3,6]=>35 [5,1,4,2,6,3]=>61 [5,1,4,3,2,6]=>40 [5,1,4,3,6,2]=>61 [5,1,4,6,2,3]=>40 [5,1,4,6,3,2]=>26 [5,1,6,2,3,4]=>35 [5,1,6,2,4,3]=>61 [5,1,6,3,2,4]=>40 [5,1,6,3,4,2]=>61 [5,1,6,4,2,3]=>40 [5,1,6,4,3,2]=>14 [5,2,1,3,4,6]=>10 [5,2,1,3,6,4]=>26 [5,2,1,4,3,6]=>35 [5,2,1,4,6,3]=>26 [5,2,1,6,3,4]=>35 [5,2,1,6,4,3]=>19 [5,2,3,1,4,6]=>35 [5,2,3,1,6,4]=>61 [5,2,3,4,1,6]=>40 [5,2,3,4,6,1]=>19 [5,2,3,6,1,4]=>40 [5,2,3,6,4,1]=>26 [5,2,4,1,3,6]=>35 [5,2,4,1,6,3]=>61 [5,2,4,3,1,6]=>40 [5,2,4,3,6,1]=>61 [5,2,4,6,1,3]=>40 [5,2,4,6,3,1]=>26 [5,2,6,1,3,4]=>35 [5,2,6,1,4,3]=>61 [5,2,6,3,1,4]=>40 [5,2,6,3,4,1]=>61 [5,2,6,4,1,3]=>40 [5,2,6,4,3,1]=>14 [5,3,1,2,4,6]=>10 [5,3,1,2,6,4]=>26 [5,3,1,4,2,6]=>35 [5,3,1,4,6,2]=>26 [5,3,1,6,2,4]=>35 [5,3,1,6,4,2]=>19 [5,3,2,1,4,6]=>10 [5,3,2,1,6,4]=>14 [5,3,2,4,1,6]=>35 [5,3,2,4,6,1]=>26 [5,3,2,6,1,4]=>35 [5,3,2,6,4,1]=>19 [5,3,4,1,2,6]=>35 [5,3,4,1,6,2]=>61 [5,3,4,2,1,6]=>40 [5,3,4,2,6,1]=>61 [5,3,4,6,1,2]=>40 [5,3,4,6,2,1]=>26 [5,3,6,1,2,4]=>35 [5,3,6,1,4,2]=>61 [5,3,6,2,1,4]=>40 [5,3,6,2,4,1]=>61 [5,3,6,4,1,2]=>40 [5,3,6,4,2,1]=>14 [5,4,1,2,3,6]=>10 [5,4,1,2,6,3]=>26 [5,4,1,3,2,6]=>35 [5,4,1,3,6,2]=>26 [5,4,1,6,2,3]=>35 [5,4,1,6,3,2]=>19 [5,4,2,1,3,6]=>10 [5,4,2,1,6,3]=>14 [5,4,2,3,1,6]=>35 [5,4,2,3,6,1]=>26 [5,4,2,6,1,3]=>35 [5,4,2,6,3,1]=>19 [5,4,3,1,2,6]=>10 [5,4,3,1,6,2]=>14 [5,4,3,2,1,6]=>5 [5,4,3,2,6,1]=>14 [5,4,3,6,1,2]=>35 [5,4,3,6,2,1]=>19 [5,4,6,1,2,3]=>35 [5,4,6,1,3,2]=>61 [5,4,6,2,1,3]=>40 [5,4,6,2,3,1]=>61 [5,4,6,3,1,2]=>40 [5,4,6,3,2,1]=>14 [5,6,1,2,3,4]=>14 [5,6,1,2,4,3]=>40 [5,6,1,3,2,4]=>61 [5,6,1,3,4,2]=>40 [5,6,1,4,2,3]=>61 [5,6,1,4,3,2]=>35 [5,6,2,1,3,4]=>26 [5,6,2,1,4,3]=>40 [5,6,2,3,1,4]=>61 [5,6,2,3,4,1]=>40 [5,6,2,4,1,3]=>61 [5,6,2,4,3,1]=>35 [5,6,3,1,2,4]=>26 [5,6,3,1,4,2]=>40 [5,6,3,2,1,4]=>19 [5,6,3,2,4,1]=>40 [5,6,3,4,1,2]=>61 [5,6,3,4,2,1]=>35 [5,6,4,1,2,3]=>26 [5,6,4,1,3,2]=>40 [5,6,4,2,1,3]=>19 [5,6,4,2,3,1]=>40 [5,6,4,3,1,2]=>19 [5,6,4,3,2,1]=>5 [6,1,2,3,4,5]=>5 [6,1,2,3,5,4]=>19 [6,1,2,4,3,5]=>40 [6,1,2,4,5,3]=>19 [6,1,2,5,3,4]=>40 [6,1,2,5,4,3]=>26 [6,1,3,2,4,5]=>35 [6,1,3,2,5,4]=>61 [6,1,3,4,2,5]=>40 [6,1,3,4,5,2]=>19 [6,1,3,5,2,4]=>40 [6,1,3,5,4,2]=>26 [6,1,4,2,3,5]=>35 [6,1,4,2,5,3]=>61 [6,1,4,3,2,5]=>40 [6,1,4,3,5,2]=>61 [6,1,4,5,2,3]=>40 [6,1,4,5,3,2]=>26 [6,1,5,2,3,4]=>35 [6,1,5,2,4,3]=>61 [6,1,5,3,2,4]=>40 [6,1,5,3,4,2]=>61 [6,1,5,4,2,3]=>40 [6,1,5,4,3,2]=>14 [6,2,1,3,4,5]=>10 [6,2,1,3,5,4]=>26 [6,2,1,4,3,5]=>35 [6,2,1,4,5,3]=>26 [6,2,1,5,3,4]=>35 [6,2,1,5,4,3]=>19 [6,2,3,1,4,5]=>35 [6,2,3,1,5,4]=>61 [6,2,3,4,1,5]=>40 [6,2,3,4,5,1]=>19 [6,2,3,5,1,4]=>40 [6,2,3,5,4,1]=>26 [6,2,4,1,3,5]=>35 [6,2,4,1,5,3]=>61 [6,2,4,3,1,5]=>40 [6,2,4,3,5,1]=>61 [6,2,4,5,1,3]=>40 [6,2,4,5,3,1]=>26 [6,2,5,1,3,4]=>35 [6,2,5,1,4,3]=>61 [6,2,5,3,1,4]=>40 [6,2,5,3,4,1]=>61 [6,2,5,4,1,3]=>40 [6,2,5,4,3,1]=>14 [6,3,1,2,4,5]=>10 [6,3,1,2,5,4]=>26 [6,3,1,4,2,5]=>35 [6,3,1,4,5,2]=>26 [6,3,1,5,2,4]=>35 [6,3,1,5,4,2]=>19 [6,3,2,1,4,5]=>10 [6,3,2,1,5,4]=>14 [6,3,2,4,1,5]=>35 [6,3,2,4,5,1]=>26 [6,3,2,5,1,4]=>35 [6,3,2,5,4,1]=>19 [6,3,4,1,2,5]=>35 [6,3,4,1,5,2]=>61 [6,3,4,2,1,5]=>40 [6,3,4,2,5,1]=>61 [6,3,4,5,1,2]=>40 [6,3,4,5,2,1]=>26 [6,3,5,1,2,4]=>35 [6,3,5,1,4,2]=>61 [6,3,5,2,1,4]=>40 [6,3,5,2,4,1]=>61 [6,3,5,4,1,2]=>40 [6,3,5,4,2,1]=>14 [6,4,1,2,3,5]=>10 [6,4,1,2,5,3]=>26 [6,4,1,3,2,5]=>35 [6,4,1,3,5,2]=>26 [6,4,1,5,2,3]=>35 [6,4,1,5,3,2]=>19 [6,4,2,1,3,5]=>10 [6,4,2,1,5,3]=>14 [6,4,2,3,1,5]=>35 [6,4,2,3,5,1]=>26 [6,4,2,5,1,3]=>35 [6,4,2,5,3,1]=>19 [6,4,3,1,2,5]=>10 [6,4,3,1,5,2]=>14 [6,4,3,2,1,5]=>5 [6,4,3,2,5,1]=>14 [6,4,3,5,1,2]=>35 [6,4,3,5,2,1]=>19 [6,4,5,1,2,3]=>35 [6,4,5,1,3,2]=>61 [6,4,5,2,1,3]=>40 [6,4,5,2,3,1]=>61 [6,4,5,3,1,2]=>40 [6,4,5,3,2,1]=>14 [6,5,1,2,3,4]=>10 [6,5,1,2,4,3]=>26 [6,5,1,3,2,4]=>35 [6,5,1,3,4,2]=>26 [6,5,1,4,2,3]=>35 [6,5,1,4,3,2]=>19 [6,5,2,1,3,4]=>10 [6,5,2,1,4,3]=>14 [6,5,2,3,1,4]=>35 [6,5,2,3,4,1]=>26 [6,5,2,4,1,3]=>35 [6,5,2,4,3,1]=>19 [6,5,3,1,2,4]=>10 [6,5,3,1,4,2]=>14 [6,5,3,2,1,4]=>5 [6,5,3,2,4,1]=>14 [6,5,3,4,1,2]=>35 [6,5,3,4,2,1]=>19 [6,5,4,1,2,3]=>10 [6,5,4,1,3,2]=>14 [6,5,4,2,1,3]=>5 [6,5,4,2,3,1]=>14 [6,5,4,3,1,2]=>5 [6,5,4,3,2,1]=>1 [1,2,3,4,5,6,7]=>1 [1,2,3,4,5,7,6]=>6 [1,2,3,4,6,5,7]=>20 [1,2,3,4,6,7,5]=>6 [1,2,3,4,7,5,6]=>20 [1,2,3,4,7,6,5]=>15 [1,2,3,5,4,6,7]=>34 [1,2,3,5,4,7,6]=>64 [1,2,3,5,6,4,7]=>20 [1,2,3,5,6,7,4]=>6 [1,2,3,5,7,4,6]=>20 [1,2,3,5,7,6,4]=>15 [1,2,3,6,4,5,7]=>34 [1,2,3,6,4,7,5]=>64 [1,2,3,6,5,4,7]=>50 [1,2,3,6,5,7,4]=>64 [1,2,3,6,7,4,5]=>20 [1,2,3,6,7,5,4]=>15 [1,2,3,7,4,5,6]=>34 [1,2,3,7,4,6,5]=>64 [1,2,3,7,5,4,6]=>50 [1,2,3,7,5,6,4]=>64 [1,2,3,7,6,4,5]=>50 [1,2,3,7,6,5,4]=>20 [1,2,4,3,5,6,7]=>34 [1,2,4,3,5,7,6]=>99 [1,2,4,3,6,5,7]=>155 [1,2,4,3,6,7,5]=>99 [1,2,4,3,7,5,6]=>155 [1,2,4,3,7,6,5]=>90 [1,2,4,5,3,6,7]=>34 [1,2,4,5,3,7,6]=>64 [1,2,4,5,6,3,7]=>20 [1,2,4,5,6,7,3]=>6 [1,2,4,5,7,3,6]=>20 [1,2,4,5,7,6,3]=>15 [1,2,4,6,3,5,7]=>34 [1,2,4,6,3,7,5]=>64 [1,2,4,6,5,3,7]=>50 [1,2,4,6,5,7,3]=>64 [1,2,4,6,7,3,5]=>20 [1,2,4,6,7,5,3]=>15 [1,2,4,7,3,5,6]=>34 [1,2,4,7,3,6,5]=>64 [1,2,4,7,5,3,6]=>50 [1,2,4,7,5,6,3]=>64 [1,2,4,7,6,3,5]=>50 [1,2,4,7,6,5,3]=>20 [1,2,5,3,4,6,7]=>34 [1,2,5,3,4,7,6]=>99 [1,2,5,3,6,4,7]=>155 [1,2,5,3,6,7,4]=>99 [1,2,5,3,7,4,6]=>155 [1,2,5,3,7,6,4]=>90 [1,2,5,4,3,6,7]=>71 [1,2,5,4,3,7,6]=>111 [1,2,5,4,6,3,7]=>155 [1,2,5,4,6,7,3]=>99 [1,2,5,4,7,3,6]=>155 [1,2,5,4,7,6,3]=>90 [1,2,5,6,3,4,7]=>34 [1,2,5,6,3,7,4]=>64 [1,2,5,6,4,3,7]=>50 [1,2,5,6,4,7,3]=>64 [1,2,5,6,7,3,4]=>20 [1,2,5,6,7,4,3]=>15 [1,2,5,7,3,4,6]=>34 [1,2,5,7,3,6,4]=>64 [1,2,5,7,4,3,6]=>50 [1,2,5,7,4,6,3]=>64 [1,2,5,7,6,3,4]=>50 [1,2,5,7,6,4,3]=>20 [1,2,6,3,4,5,7]=>34 [1,2,6,3,4,7,5]=>99 [1,2,6,3,5,4,7]=>155 [1,2,6,3,5,7,4]=>99 [1,2,6,3,7,4,5]=>155 [1,2,6,3,7,5,4]=>90 [1,2,6,4,3,5,7]=>71 [1,2,6,4,3,7,5]=>111 [1,2,6,4,5,3,7]=>155 [1,2,6,4,5,7,3]=>99 [1,2,6,4,7,3,5]=>155 [1,2,6,4,7,5,3]=>90 [1,2,6,5,3,4,7]=>71 [1,2,6,5,3,7,4]=>111 [1,2,6,5,4,3,7]=>55 [1,2,6,5,4,7,3]=>111 [1,2,6,5,7,3,4]=>155 [1,2,6,5,7,4,3]=>90 [1,2,6,7,3,4,5]=>34 [1,2,6,7,3,5,4]=>64 [1,2,6,7,4,3,5]=>50 [1,2,6,7,4,5,3]=>64 [1,2,6,7,5,3,4]=>50 [1,2,6,7,5,4,3]=>20 [1,2,7,3,4,5,6]=>34 [1,2,7,3,4,6,5]=>99 [1,2,7,3,5,4,6]=>155 [1,2,7,3,5,6,4]=>99 [1,2,7,3,6,4,5]=>155 [1,2,7,3,6,5,4]=>90 [1,2,7,4,3,5,6]=>71 [1,2,7,4,3,6,5]=>111 [1,2,7,4,5,3,6]=>155 [1,2,7,4,5,6,3]=>99 [1,2,7,4,6,3,5]=>155 [1,2,7,4,6,5,3]=>90 [1,2,7,5,3,4,6]=>71 [1,2,7,5,3,6,4]=>111 [1,2,7,5,4,3,6]=>55 [1,2,7,5,4,6,3]=>111 [1,2,7,5,6,3,4]=>155 [1,2,7,5,6,4,3]=>90 [1,2,7,6,3,4,5]=>71 [1,2,7,6,3,5,4]=>111 [1,2,7,6,4,3,5]=>55 [1,2,7,6,4,5,3]=>111 [1,2,7,6,5,3,4]=>55 [1,2,7,6,5,4,3]=>15 [1,3,2,4,5,6,7]=>20 [1,3,2,4,5,7,6]=>78 [1,3,2,4,6,5,7]=>169 [1,3,2,4,6,7,5]=>78 [1,3,2,4,7,5,6]=>169 [1,3,2,4,7,6,5]=>111 [1,3,2,5,4,6,7]=>155 [1,3,2,5,4,7,6]=>272 [1,3,2,5,6,4,7]=>169 [1,3,2,5,6,7,4]=>78 [1,3,2,5,7,4,6]=>169 [1,3,2,5,7,6,4]=>111 [1,3,2,6,4,5,7]=>155 [1,3,2,6,4,7,5]=>272 [1,3,2,6,5,4,7]=>181 [1,3,2,6,5,7,4]=>272 [1,3,2,6,7,4,5]=>169 [1,3,2,6,7,5,4]=>111 [1,3,2,7,4,5,6]=>155 [1,3,2,7,4,6,5]=>272 [1,3,2,7,5,4,6]=>181 [1,3,2,7,5,6,4]=>272 [1,3,2,7,6,4,5]=>181 [1,3,2,7,6,5,4]=>64 [1,3,4,2,5,6,7]=>34 [1,3,4,2,5,7,6]=>99 [1,3,4,2,6,5,7]=>155 [1,3,4,2,6,7,5]=>99 [1,3,4,2,7,5,6]=>155 [1,3,4,2,7,6,5]=>90 [1,3,4,5,2,6,7]=>34 [1,3,4,5,2,7,6]=>64 [1,3,4,5,6,2,7]=>20 [1,3,4,5,6,7,2]=>6 [1,3,4,5,7,2,6]=>20 [1,3,4,5,7,6,2]=>15 [1,3,4,6,2,5,7]=>34 [1,3,4,6,2,7,5]=>64 [1,3,4,6,5,2,7]=>50 [1,3,4,6,5,7,2]=>64 [1,3,4,6,7,2,5]=>20 [1,3,4,6,7,5,2]=>15 [1,3,4,7,2,5,6]=>34 [1,3,4,7,2,6,5]=>64 [1,3,4,7,5,2,6]=>50 [1,3,4,7,5,6,2]=>64 [1,3,4,7,6,2,5]=>50 [1,3,4,7,6,5,2]=>20 [1,3,5,2,4,6,7]=>34 [1,3,5,2,4,7,6]=>99 [1,3,5,2,6,4,7]=>155 [1,3,5,2,6,7,4]=>99 [1,3,5,2,7,4,6]=>155 [1,3,5,2,7,6,4]=>90 [1,3,5,4,2,6,7]=>71 [1,3,5,4,2,7,6]=>111 [1,3,5,4,6,2,7]=>155 [1,3,5,4,6,7,2]=>99 [1,3,5,4,7,2,6]=>155 [1,3,5,4,7,6,2]=>90 [1,3,5,6,2,4,7]=>34 [1,3,5,6,2,7,4]=>64 [1,3,5,6,4,2,7]=>50 [1,3,5,6,4,7,2]=>64 [1,3,5,6,7,2,4]=>20 [1,3,5,6,7,4,2]=>15 [1,3,5,7,2,4,6]=>34 [1,3,5,7,2,6,4]=>64 [1,3,5,7,4,2,6]=>50 [1,3,5,7,4,6,2]=>64 [1,3,5,7,6,2,4]=>50 [1,3,5,7,6,4,2]=>20 [1,3,6,2,4,5,7]=>34 [1,3,6,2,4,7,5]=>99 [1,3,6,2,5,4,7]=>155 [1,3,6,2,5,7,4]=>99 [1,3,6,2,7,4,5]=>155 [1,3,6,2,7,5,4]=>90 [1,3,6,4,2,5,7]=>71 [1,3,6,4,2,7,5]=>111 [1,3,6,4,5,2,7]=>155 [1,3,6,4,5,7,2]=>99 [1,3,6,4,7,2,5]=>155 [1,3,6,4,7,5,2]=>90 [1,3,6,5,2,4,7]=>71 [1,3,6,5,2,7,4]=>111 [1,3,6,5,4,2,7]=>55 [1,3,6,5,4,7,2]=>111 [1,3,6,5,7,2,4]=>155 [1,3,6,5,7,4,2]=>90 [1,3,6,7,2,4,5]=>34 [1,3,6,7,2,5,4]=>64 [1,3,6,7,4,2,5]=>50 [1,3,6,7,4,5,2]=>64 [1,3,6,7,5,2,4]=>50 [1,3,6,7,5,4,2]=>20 [1,3,7,2,4,5,6]=>34 [1,3,7,2,4,6,5]=>99 [1,3,7,2,5,4,6]=>155 [1,3,7,2,5,6,4]=>99 [1,3,7,2,6,4,5]=>155 [1,3,7,2,6,5,4]=>90 [1,3,7,4,2,5,6]=>71 [1,3,7,4,2,6,5]=>111 [1,3,7,4,5,2,6]=>155 [1,3,7,4,5,6,2]=>99 [1,3,7,4,6,2,5]=>155 [1,3,7,4,6,5,2]=>90 [1,3,7,5,2,4,6]=>71 [1,3,7,5,2,6,4]=>111 [1,3,7,5,4,2,6]=>55 [1,3,7,5,4,6,2]=>111 [1,3,7,5,6,2,4]=>155 [1,3,7,5,6,4,2]=>90 [1,3,7,6,2,4,5]=>71 [1,3,7,6,2,5,4]=>111 [1,3,7,6,4,2,5]=>55 [1,3,7,6,4,5,2]=>111 [1,3,7,6,5,2,4]=>55 [1,3,7,6,5,4,2]=>15 [1,4,2,3,5,6,7]=>20 [1,4,2,3,5,7,6]=>78 [1,4,2,3,6,5,7]=>169 [1,4,2,3,6,7,5]=>78 [1,4,2,3,7,5,6]=>169 [1,4,2,3,7,6,5]=>111 [1,4,2,5,3,6,7]=>155 [1,4,2,5,3,7,6]=>272 [1,4,2,5,6,3,7]=>169 [1,4,2,5,6,7,3]=>78 [1,4,2,5,7,3,6]=>169 [1,4,2,5,7,6,3]=>111 [1,4,2,6,3,5,7]=>155 [1,4,2,6,3,7,5]=>272 [1,4,2,6,5,3,7]=>181 [1,4,2,6,5,7,3]=>272 [1,4,2,6,7,3,5]=>169 [1,4,2,6,7,5,3]=>111 [1,4,2,7,3,5,6]=>155 [1,4,2,7,3,6,5]=>272 [1,4,2,7,5,3,6]=>181 [1,4,2,7,5,6,3]=>272 [1,4,2,7,6,3,5]=>181 [1,4,2,7,6,5,3]=>64 [1,4,3,2,5,6,7]=>50 [1,4,3,2,5,7,6]=>132 [1,4,3,2,6,5,7]=>181 [1,4,3,2,6,7,5]=>132 [1,4,3,2,7,5,6]=>181 [1,4,3,2,7,6,5]=>99 [1,4,3,5,2,6,7]=>155 [1,4,3,5,2,7,6]=>272 [1,4,3,5,6,2,7]=>169 [1,4,3,5,6,7,2]=>78 [1,4,3,5,7,2,6]=>169 [1,4,3,5,7,6,2]=>111 [1,4,3,6,2,5,7]=>155 [1,4,3,6,2,7,5]=>272 [1,4,3,6,5,2,7]=>181 [1,4,3,6,5,7,2]=>272 [1,4,3,6,7,2,5]=>169 [1,4,3,6,7,5,2]=>111 [1,4,3,7,2,5,6]=>155 [1,4,3,7,2,6,5]=>272 [1,4,3,7,5,2,6]=>181 [1,4,3,7,5,6,2]=>272 [1,4,3,7,6,2,5]=>181 [1,4,3,7,6,5,2]=>64 [1,4,5,2,3,6,7]=>34 [1,4,5,2,3,7,6]=>99 [1,4,5,2,6,3,7]=>155 [1,4,5,2,6,7,3]=>99 [1,4,5,2,7,3,6]=>155 [1,4,5,2,7,6,3]=>90 [1,4,5,3,2,6,7]=>71 [1,4,5,3,2,7,6]=>111 [1,4,5,3,6,2,7]=>155 [1,4,5,3,6,7,2]=>99 [1,4,5,3,7,2,6]=>155 [1,4,5,3,7,6,2]=>90 [1,4,5,6,2,3,7]=>34 [1,4,5,6,2,7,3]=>64 [1,4,5,6,3,2,7]=>50 [1,4,5,6,3,7,2]=>64 [1,4,5,6,7,2,3]=>20 [1,4,5,6,7,3,2]=>15 [1,4,5,7,2,3,6]=>34 [1,4,5,7,2,6,3]=>64 [1,4,5,7,3,2,6]=>50 [1,4,5,7,3,6,2]=>64 [1,4,5,7,6,2,3]=>50 [1,4,5,7,6,3,2]=>20 [1,4,6,2,3,5,7]=>34 [1,4,6,2,3,7,5]=>99 [1,4,6,2,5,3,7]=>155 [1,4,6,2,5,7,3]=>99 [1,4,6,2,7,3,5]=>155 [1,4,6,2,7,5,3]=>90 [1,4,6,3,2,5,7]=>71 [1,4,6,3,2,7,5]=>111 [1,4,6,3,5,2,7]=>155 [1,4,6,3,5,7,2]=>99 [1,4,6,3,7,2,5]=>155 [1,4,6,3,7,5,2]=>90 [1,4,6,5,2,3,7]=>71 [1,4,6,5,2,7,3]=>111 [1,4,6,5,3,2,7]=>55 [1,4,6,5,3,7,2]=>111
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Description
The number of permutations with the same descent word as the given permutation.
The descent word of a permutation is the binary word given by Mp00109descent word. For a given permutation, this statistic is the number of permutations with the same descent word, so the number of elements in the fiber of the map Mp00109descent word containing a given permutation.
This statistic appears as up-down analysis in statistical applications in genetics, see [1] and the references therein.
References
[1] Morton, J., Pachter, L., Shiu, A., Sturmfels, B., Wienand, O. Convex rank tests and semigraphoids MathSciNet:2538642
Code
from collections import defaultdict

def word(pi):
    w = [0]*(len(pi)-1)
    for i in pi.descents(from_zero=True):
        w[i] = 1
    return Words([0,1])(w)

@cached_function
def preimages(n):
    D = defaultdict(int)
    for pi in Permutations(n):
        D[word(pi)] += 1
    return D


def statistic(pi):
    return preimages(len(pi))[word(pi)]

Created
Jun 10, 2016 at 08:54 by Christian Stump
Updated
Jan 15, 2018 at 08:00 by Martin Rubey