edit this statistic or download as text // json
Identifier
Values
=>
[]=>1 [1]=>1 [1,2]=>1 [2,1]=>1 [1,2,3]=>1 [1,3,2]=>1 [2,1,3]=>1 [2,3,1]=>1 [3,1,2]=>1 [3,2,1]=>2 [1,2,3,4]=>1 [1,2,4,3]=>1 [1,3,2,4]=>1 [1,3,4,2]=>1 [1,4,2,3]=>1 [1,4,3,2]=>2 [2,1,3,4]=>1 [2,1,4,3]=>2 [2,3,1,4]=>1 [2,3,4,1]=>1 [2,4,1,3]=>2 [2,4,3,1]=>3 [3,1,2,4]=>1 [3,1,4,2]=>2 [3,2,1,4]=>2 [3,2,4,1]=>3 [3,4,1,2]=>2 [3,4,2,1]=>5 [4,1,2,3]=>1 [4,1,3,2]=>3 [4,2,1,3]=>3 [4,2,3,1]=>6 [4,3,1,2]=>5 [4,3,2,1]=>16 [1,2,3,4,5]=>1 [1,2,3,5,4]=>1 [1,2,4,3,5]=>1 [1,2,4,5,3]=>1 [1,2,5,3,4]=>1 [1,2,5,4,3]=>2 [1,3,2,4,5]=>1 [1,3,2,5,4]=>2 [1,3,4,2,5]=>1 [1,3,4,5,2]=>1 [1,3,5,2,4]=>2 [1,3,5,4,2]=>3 [1,4,2,3,5]=>1 [1,4,2,5,3]=>2 [1,4,3,2,5]=>2 [1,4,3,5,2]=>3 [1,4,5,2,3]=>2 [1,4,5,3,2]=>5 [1,5,2,3,4]=>1 [1,5,2,4,3]=>3 [1,5,3,2,4]=>3 [1,5,3,4,2]=>6 [1,5,4,2,3]=>5 [1,5,4,3,2]=>16 [2,1,3,4,5]=>1 [2,1,3,5,4]=>2 [2,1,4,3,5]=>2 [2,1,4,5,3]=>3 [2,1,5,3,4]=>3 [2,1,5,4,3]=>8 [2,3,1,4,5]=>1 [2,3,1,5,4]=>3 [2,3,4,1,5]=>1 [2,3,4,5,1]=>1 [2,3,5,1,4]=>3 [2,3,5,4,1]=>4 [2,4,1,3,5]=>2 [2,4,1,5,3]=>5 [2,4,3,1,5]=>3 [2,4,3,5,1]=>4 [2,4,5,1,3]=>5 [2,4,5,3,1]=>9 [2,5,1,3,4]=>3 [2,5,1,4,3]=>11 [2,5,3,1,4]=>6 [2,5,3,4,1]=>10 [2,5,4,1,3]=>16 [2,5,4,3,1]=>35 [3,1,2,4,5]=>1 [3,1,2,5,4]=>3 [3,1,4,2,5]=>2 [3,1,4,5,2]=>3 [3,1,5,2,4]=>5 [3,1,5,4,2]=>11 [3,2,1,4,5]=>2 [3,2,1,5,4]=>8 [3,2,4,1,5]=>3 [3,2,4,5,1]=>4 [3,2,5,1,4]=>11 [3,2,5,4,1]=>19 [3,4,1,2,5]=>2 [3,4,1,5,2]=>5 [3,4,2,1,5]=>5 [3,4,2,5,1]=>9 [3,4,5,1,2]=>5 [3,4,5,2,1]=>14 [3,5,1,2,4]=>5 [3,5,1,4,2]=>16 [3,5,2,1,4]=>16 [3,5,2,4,1]=>35 [3,5,4,1,2]=>21 [3,5,4,2,1]=>70 [4,1,2,3,5]=>1 [4,1,2,5,3]=>3 [4,1,3,2,5]=>3 [4,1,3,5,2]=>6 [4,1,5,2,3]=>5 [4,1,5,3,2]=>16 [4,2,1,3,5]=>3 [4,2,1,5,3]=>11 [4,2,3,1,5]=>6 [4,2,3,5,1]=>10 [4,2,5,1,3]=>16 [4,2,5,3,1]=>35 [4,3,1,2,5]=>5 [4,3,1,5,2]=>16 [4,3,2,1,5]=>16 [4,3,2,5,1]=>35 [4,3,5,1,2]=>21 [4,3,5,2,1]=>70 [4,5,1,2,3]=>5 [4,5,1,3,2]=>21 [4,5,2,1,3]=>21 [4,5,2,3,1]=>56 [4,5,3,1,2]=>42 [4,5,3,2,1]=>168 [5,1,2,3,4]=>1 [5,1,2,4,3]=>4 [5,1,3,2,4]=>4 [5,1,3,4,2]=>10 [5,1,4,2,3]=>9 [5,1,4,3,2]=>35 [5,2,1,3,4]=>4 [5,2,1,4,3]=>19 [5,2,3,1,4]=>10 [5,2,3,4,1]=>20 [5,2,4,1,3]=>35 [5,2,4,3,1]=>90 [5,3,1,2,4]=>9 [5,3,1,4,2]=>35 [5,3,2,1,4]=>35 [5,3,2,4,1]=>90 [5,3,4,1,2]=>56 [5,3,4,2,1]=>216 [5,4,1,2,3]=>14 [5,4,1,3,2]=>70 [5,4,2,1,3]=>70 [5,4,2,3,1]=>216 [5,4,3,1,2]=>168 [5,4,3,2,1]=>768 [1,2,3,4,5,6]=>1 [1,2,3,4,6,5]=>1 [1,2,3,5,4,6]=>1 [1,2,3,5,6,4]=>1 [1,2,3,6,4,5]=>1 [1,2,3,6,5,4]=>2 [1,2,4,3,5,6]=>1 [1,2,4,3,6,5]=>2 [1,2,4,5,3,6]=>1 [1,2,4,5,6,3]=>1 [1,2,4,6,3,5]=>2 [1,2,4,6,5,3]=>3 [1,2,5,3,4,6]=>1 [1,2,5,3,6,4]=>2 [1,2,5,4,3,6]=>2 [1,2,5,4,6,3]=>3 [1,2,5,6,3,4]=>2 [1,2,5,6,4,3]=>5 [1,2,6,3,4,5]=>1 [1,2,6,3,5,4]=>3 [1,2,6,4,3,5]=>3 [1,2,6,4,5,3]=>6 [1,2,6,5,3,4]=>5 [1,2,6,5,4,3]=>16 [1,3,2,4,5,6]=>1 [1,3,2,4,6,5]=>2 [1,3,2,5,4,6]=>2 [1,3,2,5,6,4]=>3 [1,3,2,6,4,5]=>3 [1,3,2,6,5,4]=>8 [1,3,4,2,5,6]=>1 [1,3,4,2,6,5]=>3 [1,3,4,5,2,6]=>1 [1,3,4,5,6,2]=>1 [1,3,4,6,2,5]=>3 [1,3,4,6,5,2]=>4 [1,3,5,2,4,6]=>2 [1,3,5,2,6,4]=>5 [1,3,5,4,2,6]=>3 [1,3,5,4,6,2]=>4 [1,3,5,6,2,4]=>5 [1,3,5,6,4,2]=>9 [1,3,6,2,4,5]=>3 [1,3,6,2,5,4]=>11 [1,3,6,4,2,5]=>6 [1,3,6,4,5,2]=>10 [1,3,6,5,2,4]=>16 [1,3,6,5,4,2]=>35 [1,4,2,3,5,6]=>1 [1,4,2,3,6,5]=>3 [1,4,2,5,3,6]=>2 [1,4,2,5,6,3]=>3 [1,4,2,6,3,5]=>5 [1,4,2,6,5,3]=>11 [1,4,3,2,5,6]=>2 [1,4,3,2,6,5]=>8 [1,4,3,5,2,6]=>3 [1,4,3,5,6,2]=>4 [1,4,3,6,2,5]=>11 [1,4,3,6,5,2]=>19 [1,4,5,2,3,6]=>2 [1,4,5,2,6,3]=>5 [1,4,5,3,2,6]=>5 [1,4,5,3,6,2]=>9 [1,4,5,6,2,3]=>5 [1,4,5,6,3,2]=>14 [1,4,6,2,3,5]=>5 [1,4,6,2,5,3]=>16 [1,4,6,3,2,5]=>16 [1,4,6,3,5,2]=>35 [1,4,6,5,2,3]=>21 [1,4,6,5,3,2]=>70 [1,5,2,3,4,6]=>1 [1,5,2,3,6,4]=>3 [1,5,2,4,3,6]=>3 [1,5,2,4,6,3]=>6 [1,5,2,6,3,4]=>5 [1,5,2,6,4,3]=>16 [1,5,3,2,4,6]=>3 [1,5,3,2,6,4]=>11 [1,5,3,4,2,6]=>6 [1,5,3,4,6,2]=>10 [1,5,3,6,2,4]=>16 [1,5,3,6,4,2]=>35 [1,5,4,2,3,6]=>5 [1,5,4,2,6,3]=>16 [1,5,4,3,2,6]=>16 [1,5,4,3,6,2]=>35 [1,5,4,6,2,3]=>21 [1,5,4,6,3,2]=>70 [1,5,6,2,3,4]=>5 [1,5,6,2,4,3]=>21 [1,5,6,3,2,4]=>21 [1,5,6,3,4,2]=>56 [1,5,6,4,2,3]=>42 [1,5,6,4,3,2]=>168 [1,6,2,3,4,5]=>1 [1,6,2,3,5,4]=>4 [1,6,2,4,3,5]=>4 [1,6,2,4,5,3]=>10 [1,6,2,5,3,4]=>9 [1,6,2,5,4,3]=>35 [1,6,3,2,4,5]=>4 [1,6,3,2,5,4]=>19 [1,6,3,4,2,5]=>10 [1,6,3,4,5,2]=>20 [1,6,3,5,2,4]=>35 [1,6,3,5,4,2]=>90 [1,6,4,2,3,5]=>9 [1,6,4,2,5,3]=>35 [1,6,4,3,2,5]=>35 [1,6,4,3,5,2]=>90 [1,6,4,5,2,3]=>56 [1,6,4,5,3,2]=>216 [1,6,5,2,3,4]=>14 [1,6,5,2,4,3]=>70 [1,6,5,3,2,4]=>70 [1,6,5,3,4,2]=>216 [1,6,5,4,2,3]=>168 [1,6,5,4,3,2]=>768 [2,1,3,4,5,6]=>1 [2,1,3,4,6,5]=>2 [2,1,3,5,4,6]=>2 [2,1,3,5,6,4]=>3 [2,1,3,6,4,5]=>3 [2,1,3,6,5,4]=>8 [2,1,4,3,5,6]=>2 [2,1,4,3,6,5]=>6 [2,1,4,5,3,6]=>3 [2,1,4,5,6,3]=>4 [2,1,4,6,3,5]=>8 [2,1,4,6,5,3]=>15 [2,1,5,3,4,6]=>3 [2,1,5,3,6,4]=>8 [2,1,5,4,3,6]=>8 [2,1,5,4,6,3]=>15 [2,1,5,6,3,4]=>10 [2,1,5,6,4,3]=>30 [2,1,6,3,4,5]=>4 [2,1,6,3,5,4]=>15 [2,1,6,4,3,5]=>15 [2,1,6,4,5,3]=>36 [2,1,6,5,3,4]=>30 [2,1,6,5,4,3]=>112 [2,3,1,4,5,6]=>1 [2,3,1,4,6,5]=>3 [2,3,1,5,4,6]=>3 [2,3,1,5,6,4]=>6 [2,3,1,6,4,5]=>6 [2,3,1,6,5,4]=>20 [2,3,4,1,5,6]=>1 [2,3,4,1,6,5]=>4 [2,3,4,5,1,6]=>1 [2,3,4,5,6,1]=>1 [2,3,4,6,1,5]=>4 [2,3,4,6,5,1]=>5 [2,3,5,1,4,6]=>3 [2,3,5,1,6,4]=>9 [2,3,5,4,1,6]=>4 [2,3,5,4,6,1]=>5 [2,3,5,6,1,4]=>9 [2,3,5,6,4,1]=>14 [2,3,6,1,4,5]=>6 [2,3,6,1,5,4]=>26 [2,3,6,4,1,5]=>10 [2,3,6,4,5,1]=>15 [2,3,6,5,1,4]=>35 [2,3,6,5,4,1]=>64 [2,4,1,3,5,6]=>2 [2,4,1,3,6,5]=>8 [2,4,1,5,3,6]=>5 [2,4,1,5,6,3]=>9 [2,4,1,6,3,5]=>16 [2,4,1,6,5,3]=>40 [2,4,3,1,5,6]=>3 [2,4,3,1,6,5]=>15 [2,4,3,5,1,6]=>4 [2,4,3,5,6,1]=>5 [2,4,3,6,1,5]=>19 [2,4,3,6,5,1]=>29 [2,4,5,1,3,6]=>5 [2,4,5,1,6,3]=>14 [2,4,5,3,1,6]=>9 [2,4,5,3,6,1]=>14 [2,4,5,6,1,3]=>14 [2,4,5,6,3,1]=>28 [2,4,6,1,3,5]=>16 [2,4,6,1,5,3]=>56 [2,4,6,3,1,5]=>35 [2,4,6,3,5,1]=>64 [2,4,6,5,1,3]=>70 [2,4,6,5,3,1]=>162 [2,5,1,3,4,6]=>3 [2,5,1,3,6,4]=>11 [2,5,1,4,3,6]=>11 [2,5,1,4,6,3]=>26 [2,5,1,6,3,4]=>21 [2,5,1,6,4,3]=>77 [2,5,3,1,4,6]=>6 [2,5,3,1,6,4]=>26 [2,5,3,4,1,6]=>10 [2,5,3,4,6,1]=>15 [2,5,3,6,1,4]=>35 [2,5,3,6,4,1]=>64 [2,5,4,1,3,6]=>16 [2,5,4,1,6,3]=>56 [2,5,4,3,1,6]=>35 [2,5,4,3,6,1]=>64 [2,5,4,6,1,3]=>70 [2,5,4,6,3,1]=>162 [2,5,6,1,3,4]=>21 [2,5,6,1,4,3]=>98 [2,5,6,3,1,4]=>56 [2,5,6,3,4,1]=>120 [2,5,6,4,1,3]=>168 [2,5,6,4,3,1]=>450 [2,6,1,3,4,5]=>4 [2,6,1,3,5,4]=>19 [2,6,1,4,3,5]=>19 [2,6,1,4,5,3]=>55 [2,6,1,5,3,4]=>49 [2,6,1,5,4,3]=>216 [2,6,3,1,4,5]=>10 [2,6,3,1,5,4]=>55 [2,6,3,4,1,5]=>20 [2,6,3,4,5,1]=>35 [2,6,3,5,1,4]=>90 [2,6,3,5,4,1]=>189 [2,6,4,1,3,5]=>35 [2,6,4,1,5,3]=>146 [2,6,4,3,1,5]=>90 [2,6,4,3,5,1]=>189 [2,6,4,5,1,3]=>216 [2,6,4,5,3,1]=>567 [2,6,5,1,3,4]=>70 [2,6,5,1,4,3]=>384 [2,6,5,3,1,4]=>216 [2,6,5,3,4,1]=>525 [2,6,5,4,1,3]=>768 [2,6,5,4,3,1]=>2310 [3,1,2,4,5,6]=>1 [3,1,2,4,6,5]=>3 [3,1,2,5,4,6]=>3 [3,1,2,5,6,4]=>6 [3,1,2,6,4,5]=>6 [3,1,2,6,5,4]=>20 [3,1,4,2,5,6]=>2 [3,1,4,2,6,5]=>8 [3,1,4,5,2,6]=>3 [3,1,4,5,6,2]=>4 [3,1,4,6,2,5]=>11 [3,1,4,6,5,2]=>19 [3,1,5,2,4,6]=>5 [3,1,5,2,6,4]=>16 [3,1,5,4,2,6]=>11 [3,1,5,4,6,2]=>19 [3,1,5,6,2,4]=>21 [3,1,5,6,4,2]=>49 [3,1,6,2,4,5]=>9 [3,1,6,2,5,4]=>40 [3,1,6,4,2,5]=>26 [3,1,6,4,5,2]=>55 [3,1,6,5,2,4]=>77 [3,1,6,5,4,2]=>216 [3,2,1,4,5,6]=>2 [3,2,1,4,6,5]=>8 [3,2,1,5,4,6]=>8 [3,2,1,5,6,4]=>20 [3,2,1,6,4,5]=>20 [3,2,1,6,5,4]=>80 [3,2,4,1,5,6]=>3 [3,2,4,1,6,5]=>15 [3,2,4,5,1,6]=>4 [3,2,4,5,6,1]=>5 [3,2,4,6,1,5]=>19 [3,2,4,6,5,1]=>29 [3,2,5,1,4,6]=>11 [3,2,5,1,6,4]=>40 [3,2,5,4,1,6]=>19 [3,2,5,4,6,1]=>29 [3,2,5,6,1,4]=>49 [3,2,5,6,4,1]=>92 [3,2,6,1,4,5]=>26 [3,2,6,1,5,4]=>132 [3,2,6,4,1,5]=>55 [3,2,6,4,5,1]=>99 [3,2,6,5,1,4]=>216 [3,2,6,5,4,1]=>471 [3,4,1,2,5,6]=>2 [3,4,1,2,6,5]=>10 [3,4,1,5,2,6]=>5 [3,4,1,5,6,2]=>9 [3,4,1,6,2,5]=>21 [3,4,1,6,5,2]=>49 [3,4,2,1,5,6]=>5 [3,4,2,1,6,5]=>30 [3,4,2,5,1,6]=>9 [3,4,2,5,6,1]=>14 [3,4,2,6,1,5]=>49 [3,4,2,6,5,1]=>92 [3,4,5,1,2,6]=>5 [3,4,5,1,6,2]=>14 [3,4,5,2,1,6]=>14 [3,4,5,2,6,1]=>28 [3,4,5,6,1,2]=>14 [3,4,5,6,2,1]=>42 [3,4,6,1,2,5]=>21 [3,4,6,1,5,2]=>70 [3,4,6,2,1,5]=>70 [3,4,6,2,5,1]=>162 [3,4,6,5,1,2]=>84 [3,4,6,5,2,1]=>288 [3,5,1,2,4,6]=>5 [3,5,1,2,6,4]=>21 [3,5,1,4,2,6]=>16 [3,5,1,4,6,2]=>35 [3,5,1,6,2,4]=>42 [3,5,1,6,4,2]=>126 [3,5,2,1,4,6]=>16 [3,5,2,1,6,4]=>77 [3,5,2,4,1,6]=>35 [3,5,2,4,6,1]=>64 [3,5,2,6,1,4]=>126 [3,5,2,6,4,1]=>282 [3,5,4,1,2,6]=>21 [3,5,4,1,6,2]=>70 [3,5,4,2,1,6]=>70 [3,5,4,2,6,1]=>162 [3,5,4,6,1,2]=>84 [3,5,4,6,2,1]=>288 [3,5,6,1,2,4]=>42 [3,5,6,1,4,2]=>168 [3,5,6,2,1,4]=>168 [3,5,6,2,4,1]=>450 [3,5,6,4,1,2]=>252 [3,5,6,4,2,1]=>990 [3,6,1,2,4,5]=>9 [3,6,1,2,5,4]=>49 [3,6,1,4,2,5]=>35 [3,6,1,4,5,2]=>90 [3,6,1,5,2,4]=>126 [3,6,1,5,4,2]=>432 [3,6,2,1,4,5]=>35 [3,6,2,1,5,4]=>216 [3,6,2,4,1,5]=>90 [3,6,2,4,5,1]=>189 [3,6,2,5,1,4]=>432 [3,6,2,5,4,1]=>1092 [3,6,4,1,2,5]=>56 [3,6,4,1,5,2]=>216 [3,6,4,2,1,5]=>216 [3,6,4,2,5,1]=>567 [3,6,4,5,1,2]=>300 [3,6,4,5,2,1]=>1155 [3,6,5,1,2,4]=>168 [3,6,5,1,4,2]=>768 [3,6,5,2,1,4]=>768 [3,6,5,2,4,1]=>2310 [3,6,5,4,1,2]=>1320 [3,6,5,4,2,1]=>5775 [4,1,2,3,5,6]=>1 [4,1,2,3,6,5]=>4 [4,1,2,5,3,6]=>3 [4,1,2,5,6,3]=>6 [4,1,2,6,3,5]=>9 [4,1,2,6,5,3]=>26 [4,1,3,2,5,6]=>3 [4,1,3,2,6,5]=>15 [4,1,3,5,2,6]=>6 [4,1,3,5,6,2]=>10 [4,1,3,6,2,5]=>26 [4,1,3,6,5,2]=>55 [4,1,5,2,3,6]=>5 [4,1,5,2,6,3]=>16 [4,1,5,3,2,6]=>16 [4,1,5,3,6,2]=>35 [4,1,5,6,2,3]=>21 [4,1,5,6,3,2]=>70 [4,1,6,2,3,5]=>14 [4,1,6,2,5,3]=>56 [4,1,6,3,2,5]=>56 [4,1,6,3,5,2]=>146 [4,1,6,5,2,3]=>98 [4,1,6,5,3,2]=>384 [4,2,1,3,5,6]=>3 [4,2,1,3,6,5]=>15 [4,2,1,5,3,6]=>11 [4,2,1,5,6,3]=>26 [4,2,1,6,3,5]=>40 [4,2,1,6,5,3]=>132 [4,2,3,1,5,6]=>6 [4,2,3,1,6,5]=>36 [4,2,3,5,1,6]=>10 [4,2,3,5,6,1]=>15 [4,2,3,6,1,5]=>55 [4,2,3,6,5,1]=>99 [4,2,5,1,3,6]=>16 [4,2,5,1,6,3]=>56 [4,2,5,3,1,6]=>35 [4,2,5,3,6,1]=>64 [4,2,5,6,1,3]=>70 [4,2,5,6,3,1]=>162 [4,2,6,1,3,5]=>56 [4,2,6,1,5,3]=>244 [4,2,6,3,1,5]=>146 [4,2,6,3,5,1]=>309 [4,2,6,5,1,3]=>384 [4,2,6,5,3,1]=>1017 [4,3,1,2,5,6]=>5 [4,3,1,2,6,5]=>30 [4,3,1,5,2,6]=>16 [4,3,1,5,6,2]=>35 [4,3,1,6,2,5]=>77 [4,3,1,6,5,2]=>216 [4,3,2,1,5,6]=>16 [4,3,2,1,6,5]=>112 [4,3,2,5,1,6]=>35 [4,3,2,5,6,1]=>64 [4,3,2,6,1,5]=>216 [4,3,2,6,5,1]=>471 [4,3,5,1,2,6]=>21 [4,3,5,1,6,2]=>70 [4,3,5,2,1,6]=>70 [4,3,5,2,6,1]=>162 [4,3,5,6,1,2]=>84 [4,3,5,6,2,1]=>288 [4,3,6,1,2,5]=>98 [4,3,6,1,5,2]=>384 [4,3,6,2,1,5]=>384 [4,3,6,2,5,1]=>1017 [4,3,6,5,1,2]=>552 [4,3,6,5,2,1]=>2145 [4,5,1,2,3,6]=>5 [4,5,1,2,6,3]=>21 [4,5,1,3,2,6]=>21 [4,5,1,3,6,2]=>56 [4,5,1,6,2,3]=>42 [4,5,1,6,3,2]=>168 [4,5,2,1,3,6]=>21 [4,5,2,1,6,3]=>98 [4,5,2,3,1,6]=>56 [4,5,2,3,6,1]=>120 [4,5,2,6,1,3]=>168 [4,5,2,6,3,1]=>450 [4,5,3,1,2,6]=>42 [4,5,3,1,6,2]=>168 [4,5,3,2,1,6]=>168 [4,5,3,2,6,1]=>450 [4,5,3,6,1,2]=>252 [4,5,3,6,2,1]=>990 [4,5,6,1,2,3]=>42 [4,5,6,1,3,2]=>210 [4,5,6,2,1,3]=>210 [4,5,6,2,3,1]=>660 [4,5,6,3,1,2]=>462 [4,5,6,3,2,1]=>2112 [4,6,1,2,3,5]=>14 [4,6,1,2,5,3]=>70 [4,6,1,3,2,5]=>70 [4,6,1,3,5,2]=>216 [4,6,1,5,2,3]=>168 [4,6,1,5,3,2]=>768 [4,6,2,1,3,5]=>70 [4,6,2,1,5,3]=>384 [4,6,2,3,1,5]=>216 [4,6,2,3,5,1]=>525 [4,6,2,5,1,3]=>768 [4,6,2,5,3,1]=>2310 [4,6,3,1,2,5]=>168 [4,6,3,1,5,2]=>768 [4,6,3,2,1,5]=>768 [4,6,3,2,5,1]=>2310 [4,6,3,5,1,2]=>1320 [4,6,3,5,2,1]=>5775 [4,6,5,1,2,3]=>210 [4,6,5,1,3,2]=>1188 [4,6,5,2,1,3]=>1188 [4,6,5,2,3,1]=>4158 [4,6,5,3,1,2]=>2970 [4,6,5,3,2,1]=>15015 [5,1,2,3,4,6]=>1 [5,1,2,3,6,4]=>4 [5,1,2,4,3,6]=>4 [5,1,2,4,6,3]=>10 [5,1,2,6,3,4]=>9 [5,1,2,6,4,3]=>35 [5,1,3,2,4,6]=>4 [5,1,3,2,6,4]=>19 [5,1,3,4,2,6]=>10 [5,1,3,4,6,2]=>20 [5,1,3,6,2,4]=>35 [5,1,3,6,4,2]=>90 [5,1,4,2,3,6]=>9 [5,1,4,2,6,3]=>35 [5,1,4,3,2,6]=>35 [5,1,4,3,6,2]=>90 [5,1,4,6,2,3]=>56 [5,1,4,6,3,2]=>216 [5,1,6,2,3,4]=>14 [5,1,6,2,4,3]=>70 [5,1,6,3,2,4]=>70 [5,1,6,3,4,2]=>216 [5,1,6,4,2,3]=>168 [5,1,6,4,3,2]=>768 [5,2,1,3,4,6]=>4 [5,2,1,3,6,4]=>19 [5,2,1,4,3,6]=>19 [5,2,1,4,6,3]=>55 [5,2,1,6,3,4]=>49 [5,2,1,6,4,3]=>216 [5,2,3,1,4,6]=>10 [5,2,3,1,6,4]=>55 [5,2,3,4,1,6]=>20 [5,2,3,4,6,1]=>35 [5,2,3,6,1,4]=>90 [5,2,3,6,4,1]=>189 [5,2,4,1,3,6]=>35 [5,2,4,1,6,3]=>146 [5,2,4,3,1,6]=>90 [5,2,4,3,6,1]=>189 [5,2,4,6,1,3]=>216 [5,2,4,6,3,1]=>567 [5,2,6,1,3,4]=>70 [5,2,6,1,4,3]=>384 [5,2,6,3,1,4]=>216 [5,2,6,3,4,1]=>525 [5,2,6,4,1,3]=>768 [5,2,6,4,3,1]=>2310 [5,3,1,2,4,6]=>9 [5,3,1,2,6,4]=>49 [5,3,1,4,2,6]=>35 [5,3,1,4,6,2]=>90 [5,3,1,6,2,4]=>126 [5,3,1,6,4,2]=>432 [5,3,2,1,4,6]=>35 [5,3,2,1,6,4]=>216 [5,3,2,4,1,6]=>90 [5,3,2,4,6,1]=>189 [5,3,2,6,1,4]=>432 [5,3,2,6,4,1]=>1092 [5,3,4,1,2,6]=>56 [5,3,4,1,6,2]=>216 [5,3,4,2,1,6]=>216 [5,3,4,2,6,1]=>567 [5,3,4,6,1,2]=>300 [5,3,4,6,2,1]=>1155 [5,3,6,1,2,4]=>168 [5,3,6,1,4,2]=>768 [5,3,6,2,1,4]=>768 [5,3,6,2,4,1]=>2310 [5,3,6,4,1,2]=>1320 [5,3,6,4,2,1]=>5775 [5,4,1,2,3,6]=>14 [5,4,1,2,6,3]=>70 [5,4,1,3,2,6]=>70 [5,4,1,3,6,2]=>216 [5,4,1,6,2,3]=>168 [5,4,1,6,3,2]=>768 [5,4,2,1,3,6]=>70 [5,4,2,1,6,3]=>384 [5,4,2,3,1,6]=>216 [5,4,2,3,6,1]=>525 [5,4,2,6,1,3]=>768 [5,4,2,6,3,1]=>2310 [5,4,3,1,2,6]=>168 [5,4,3,1,6,2]=>768 [5,4,3,2,1,6]=>768 [5,4,3,2,6,1]=>2310 [5,4,3,6,1,2]=>1320 [5,4,3,6,2,1]=>5775 [5,4,6,1,2,3]=>210 [5,4,6,1,3,2]=>1188 [5,4,6,2,1,3]=>1188 [5,4,6,2,3,1]=>4158 [5,4,6,3,1,2]=>2970 [5,4,6,3,2,1]=>15015 [5,6,1,2,3,4]=>14 [5,6,1,2,4,3]=>84 [5,6,1,3,2,4]=>84 [5,6,1,3,4,2]=>300 [5,6,1,4,2,3]=>252 [5,6,1,4,3,2]=>1320 [5,6,2,1,3,4]=>84 [5,6,2,1,4,3]=>552 [5,6,2,3,1,4]=>300 [5,6,2,3,4,1]=>825 [5,6,2,4,1,3]=>1320 [5,6,2,4,3,1]=>4455 [5,6,3,1,2,4]=>252 [5,6,3,1,4,2]=>1320 [5,6,3,2,1,4]=>1320 [5,6,3,2,4,1]=>4455 [5,6,3,4,1,2]=>2640 [5,6,3,4,2,1]=>12870 [5,6,4,1,2,3]=>462 [5,6,4,1,3,2]=>2970 [5,6,4,2,1,3]=>2970 [5,6,4,2,3,1]=>11583 [5,6,4,3,1,2]=>8580 [5,6,4,3,2,1]=>48048 [6,1,2,3,4,5]=>1 [6,1,2,3,5,4]=>5 [6,1,2,4,3,5]=>5 [6,1,2,4,5,3]=>15 [6,1,2,5,3,4]=>14 [6,1,2,5,4,3]=>64 [6,1,3,2,4,5]=>5 [6,1,3,2,5,4]=>29 [6,1,3,4,2,5]=>15 [6,1,3,4,5,2]=>35 [6,1,3,5,2,4]=>64 [6,1,3,5,4,2]=>189 [6,1,4,2,3,5]=>14 [6,1,4,2,5,3]=>64 [6,1,4,3,2,5]=>64 [6,1,4,3,5,2]=>189 [6,1,4,5,2,3]=>120 [6,1,4,5,3,2]=>525 [6,1,5,2,3,4]=>28 [6,1,5,2,4,3]=>162 [6,1,5,3,2,4]=>162 [6,1,5,3,4,2]=>567 [6,1,5,4,2,3]=>450 [6,1,5,4,3,2]=>2310 [6,2,1,3,4,5]=>5 [6,2,1,3,5,4]=>29 [6,2,1,4,3,5]=>29 [6,2,1,4,5,3]=>99 [6,2,1,5,3,4]=>92 [6,2,1,5,4,3]=>471 [6,2,3,1,4,5]=>15 [6,2,3,1,5,4]=>99 [6,2,3,4,1,5]=>35 [6,2,3,4,5,1]=>70 [6,2,3,5,1,4]=>189 [6,2,3,5,4,1]=>448 [6,2,4,1,3,5]=>64 [6,2,4,1,5,3]=>309 [6,2,4,3,1,5]=>189 [6,2,4,3,5,1]=>448 [6,2,4,5,1,3]=>525 [6,2,4,5,3,1]=>1540 [6,2,5,1,3,4]=>162 [6,2,5,1,4,3]=>1017 [6,2,5,3,1,4]=>567 [6,2,5,3,4,1]=>1540 [6,2,5,4,1,3]=>2310 [6,2,5,4,3,1]=>7700 [6,3,1,2,4,5]=>14 [6,3,1,2,5,4]=>92 [6,3,1,4,2,5]=>64 [6,3,1,4,5,2]=>189 [6,3,1,5,2,4]=>282 [6,3,1,5,4,2]=>1092 [6,3,2,1,4,5]=>64 [6,3,2,1,5,4]=>471 [6,3,2,4,1,5]=>189 [6,3,2,4,5,1]=>448 [6,3,2,5,1,4]=>1092 [6,3,2,5,4,1]=>3080 [6,3,4,1,2,5]=>120 [6,3,4,1,5,2]=>525 [6,3,4,2,1,5]=>525 [6,3,4,2,5,1]=>1540 [6,3,4,5,1,2]=>825 [6,3,4,5,2,1]=>3520 [6,3,5,1,2,4]=>450 [6,3,5,1,4,2]=>2310 [6,3,5,2,1,4]=>2310 [6,3,5,2,4,1]=>7700 [6,3,5,4,1,2]=>4455 [6,3,5,4,2,1]=>21450 [6,4,1,2,3,5]=>28 [6,4,1,2,5,3]=>162 [6,4,1,3,2,5]=>162 [6,4,1,3,5,2]=>567 [6,4,1,5,2,3]=>450 [6,4,1,5,3,2]=>2310 [6,4,2,1,3,5]=>162 [6,4,2,1,5,3]=>1017 [6,4,2,3,1,5]=>567 [6,4,2,3,5,1]=>1540 [6,4,2,5,1,3]=>2310 [6,4,2,5,3,1]=>7700 [6,4,3,1,2,5]=>450 [6,4,3,1,5,2]=>2310 [6,4,3,2,1,5]=>2310 [6,4,3,2,5,1]=>7700 [6,4,3,5,1,2]=>4455 [6,4,3,5,2,1]=>21450 [6,4,5,1,2,3]=>660 [6,4,5,1,3,2]=>4158 [6,4,5,2,1,3]=>4158 [6,4,5,2,3,1]=>16016 [6,4,5,3,1,2]=>11583 [6,4,5,3,2,1]=>64064 [6,5,1,2,3,4]=>42 [6,5,1,2,4,3]=>288 [6,5,1,3,2,4]=>288 [6,5,1,3,4,2]=>1155 [6,5,1,4,2,3]=>990 [6,5,1,4,3,2]=>5775 [6,5,2,1,3,4]=>288 [6,5,2,1,4,3]=>2145 [6,5,2,3,1,4]=>1155 [6,5,2,3,4,1]=>3520 [6,5,2,4,1,3]=>5775 [6,5,2,4,3,1]=>21450 [6,5,3,1,2,4]=>990 [6,5,3,1,4,2]=>5775 [6,5,3,2,1,4]=>5775 [6,5,3,2,4,1]=>21450 [6,5,3,4,1,2]=>12870 [6,5,3,4,2,1]=>68640 [6,5,4,1,2,3]=>2112 [6,5,4,1,3,2]=>15015 [6,5,4,2,1,3]=>15015 [6,5,4,2,3,1]=>64064 [6,5,4,3,1,2]=>48048 [6,5,4,3,2,1]=>292864 [1,2,3,4,5,6,7]=>1 [1,2,3,4,5,7,6]=>1 [1,2,3,4,6,5,7]=>1 [1,2,3,6,4,7,5]=>2 [1,2,6,3,4,7,5]=>3 [1,3,2,4,5,6,7]=>1 [1,3,7,2,4,5,6]=>4 [1,3,7,6,5,4,2]=>2310 [1,4,6,7,2,3,5]=>42 [1,4,6,7,5,3,2]=>990 [1,4,7,2,3,5,6]=>9 [1,4,7,6,5,3,2]=>5775 [1,5,2,3,4,7,6]=>4 [1,5,2,7,3,4,6]=>14 [1,5,4,7,6,3,2]=>2145 [1,5,6,2,7,3,4]=>42 [1,5,6,4,7,3,2]=>990 [1,5,6,7,2,3,4]=>42 [1,5,6,7,4,3,2]=>2112 [1,5,7,2,3,4,6]=>14 [1,5,7,6,4,3,2]=>15015 [1,6,2,3,4,7,5]=>4 [1,6,2,3,7,4,5]=>9 [1,6,2,7,3,4,5]=>14 [1,6,5,4,3,7,2]=>2310 [1,6,5,4,7,3,2]=>5775 [1,6,5,7,4,3,2]=>15015 [1,6,7,2,3,4,5]=>14 [1,6,7,5,4,3,2]=>48048 [1,7,2,3,4,5,6]=>1 [1,7,3,5,6,4,2]=>1540 [1,7,3,6,5,4,2]=>7700 [1,7,4,3,6,5,2]=>3080 [1,7,4,5,3,6,2]=>1540 [1,7,4,5,6,3,2]=>3520 [1,7,4,6,5,3,2]=>21450 [1,7,5,4,3,6,2]=>7700 [1,7,5,4,6,3,2]=>21450 [1,7,6,4,5,3,2]=>68640 [1,7,6,5,4,3,2]=>292864 [2,1,3,4,5,6,7]=>1 [2,1,3,4,7,5,6]=>3 [2,1,3,7,4,5,6]=>4 [2,1,6,3,4,5,7]=>4 [2,1,7,3,4,5,6]=>5 [2,1,7,6,5,4,3]=>8448 [2,3,1,4,5,6,7]=>1 [2,3,4,1,5,6,7]=>1 [2,3,4,1,5,7,6]=>4 [2,3,4,5,1,6,7]=>1 [2,3,4,5,1,7,6]=>5 [2,3,4,5,6,1,7]=>1 [2,3,4,5,6,7,1]=>1 [2,3,4,5,7,1,6]=>5 [2,3,4,6,1,7,5]=>14 [2,3,4,6,7,1,5]=>14 [2,3,4,7,1,5,6]=>10 [2,3,5,6,7,1,4]=>28 [2,4,1,3,5,6,7]=>2 [2,5,1,3,4,6,7]=>3 [2,5,7,1,3,4,6]=>70 [2,6,1,3,4,5,7]=>4 [2,6,1,7,3,4,5]=>84 [2,6,5,4,3,1,7]=>2310 [2,6,7,1,3,4,5]=>84 [2,7,1,3,4,5,6]=>5 [3,1,2,4,5,6,7]=>1 [3,1,2,4,5,7,6]=>3 [3,2,1,4,5,6,7]=>2 [3,2,4,5,6,7,1]=>6 [3,4,1,2,5,6,7]=>2 [3,4,2,5,6,7,1]=>20 [3,4,5,2,6,7,1]=>48 [3,4,5,6,2,7,1]=>90 [3,4,5,6,7,1,2]=>42 [3,5,6,1,2,4,7]=>42 [3,5,6,4,2,1,7]=>990 [3,6,1,2,4,5,7]=>9 [3,6,5,4,2,1,7]=>5775 [4,1,2,3,5,6,7]=>1 [4,1,2,3,5,7,6]=>4 [4,1,6,2,3,5,7]=>14 [4,2,3,5,6,7,1]=>21 [4,2,5,1,3,6,7]=>16 [4,3,2,1,5,6,7]=>16 [4,3,2,5,6,7,1]=>105 [4,3,5,2,6,7,1]=>315 [4,3,6,5,2,1,7]=>2145 [4,5,1,6,2,3,7]=>42 [4,5,2,3,6,7,1]=>225 [4,5,3,6,2,1,7]=>990 [4,5,6,1,2,3,7]=>42 [4,5,6,3,2,1,7]=>2112 [4,6,1,2,3,5,7]=>14 [4,6,1,2,3,7,5]=>84 [4,6,5,3,2,1,7]=>15015 [5,1,2,3,4,6,7]=>1 [5,1,2,3,4,7,6]=>5 [5,1,2,3,6,4,7]=>4 [5,1,2,3,6,7,4]=>10 [5,1,2,3,7,4,6]=>14 [5,1,2,6,3,4,7]=>9 [5,1,6,2,3,4,7]=>14 [5,1,6,2,3,7,4]=>70 [5,2,3,4,6,7,1]=>56 [5,2,6,7,1,3,4]=>1188 [5,3,2,4,6,7,1]=>350 [5,3,2,6,1,4,7]=>432 [5,3,6,7,1,2,4]=>2970 [5,4,3,2,1,6,7]=>768 [5,4,3,2,1,7,6]=>8448 [5,4,3,2,6,1,7]=>2310 [5,4,3,6,2,1,7]=>5775 [5,4,6,3,2,1,7]=>15015 [5,4,6,7,1,2,3]=>3432 [5,6,1,2,3,4,7]=>14 [5,6,1,2,3,7,4]=>84 [5,6,3,4,1,2,7]=>2640 [5,6,4,3,2,1,7]=>48048 [5,6,7,1,2,3,4]=>462 [6,1,2,3,4,5,7]=>1 [6,1,2,3,4,7,5]=>5 [6,1,2,3,7,4,5]=>14 [6,1,2,7,3,4,5]=>28 [6,2,3,4,5,7,1]=>126 [6,2,4,5,3,1,7]=>1540 [6,2,5,4,3,1,7]=>7700 [6,3,2,5,4,1,7]=>3080 [6,3,4,2,5,1,7]=>1540 [6,3,4,5,2,1,7]=>3520 [6,3,4,7,1,2,5]=>4455 [6,3,5,4,2,1,7]=>21450 [6,4,3,2,5,1,7]=>7700 [6,4,3,2,7,1,5]=>58916 [6,4,3,5,2,1,7]=>21450 [6,4,5,7,1,2,3]=>15015 [6,4,7,2,5,1,3]=>292864 [6,4,7,3,5,1,2]=>640640 [6,5,3,4,2,1,7]=>68640 [6,5,4,3,2,1,7]=>292864 [6,5,7,3,4,1,2]=>1361360 [6,7,1,2,3,4,5]=>42 [6,7,3,4,1,2,5]=>21450 [6,7,4,5,1,2,3]=>171600 [7,1,2,3,4,5,6]=>1 [7,2,1,3,4,5,6]=>6 [7,2,3,1,4,5,6]=>21 [7,2,3,4,1,5,6]=>56 [7,2,3,4,5,1,6]=>126 [7,3,1,2,4,5,6]=>20 [7,3,2,1,4,5,6]=>105 [7,3,2,4,1,5,6]=>350 [7,3,4,1,2,5,6]=>225 [7,4,1,2,3,5,6]=>48 [7,4,2,1,3,5,6]=>315 [7,4,5,6,1,2,3]=>50050 [7,5,1,2,3,4,6]=>90 [7,5,6,1,2,3,4]=>9009 [7,5,6,3,4,1,2]=>6534528 [7,6,1,2,3,4,5]=>132 [7,6,4,5,1,2,3]=>972400 [7,6,5,1,2,3,4]=>30030 [1,2,3,4,5,6,7,8]=>1 [1,7,8,6,5,4,3,2]=>141892608 [1,6,8,7,5,4,3,2]=>34918884 [1,7,6,8,5,4,3,2]=>34918884 [1,6,7,8,5,4,3,2]=>3734016 [1,5,8,7,6,4,3,2]=>10720710 [1,7,6,5,8,4,3,2]=>10720710 [1,3,5,7,8,6,4,2]=>2673 [1,4,3,8,7,6,5,2]=>61204 [1,6,5,4,3,8,7,2]=>61204 [1,4,3,6,5,8,7,2]=>314 [1,2,6,7,8,5,4,3]=>2112 [1,2,3,5,6,7,8,4]=>1 [1,2,3,4,5,6,8,7]=>1 [1,4,3,2,7,6,5,8]=>80 [1,3,4,2,6,7,5,8]=>6 [1,3,2,5,4,7,6,8]=>6 [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 [1,2,4,3,6,5,7,8]=>2 [1,3,2,5,4,6,7,8]=>2 [1,2,3,5,4,6,7,8]=>1 [1,3,2,4,5,6,7,8]=>1 [1,3,2,5,4,8,6,7]=>12 [1,3,5,8,2,4,6,7]=>35 [1,3,5,6,2,7,4,8]=>14 [1,3,2,6,4,7,5,8]=>8 [1,3,2,6,4,8,5,7]=>25 [1,3,2,6,4,5,7,8]=>3 [1,3,2,7,4,8,5,6]=>30 [1,3,2,7,4,5,6,8]=>4 [1,3,2,8,4,5,6,7]=>5 [1,3,2,4,5,8,6,7]=>3 [1,4,2,5,3,7,6,8]=>8 [1,4,2,5,3,8,6,7]=>20 [1,4,2,5,3,6,7,8]=>2 [1,4,5,6,7,2,3,8]=>14 [1,4,2,6,3,7,5,8]=>16 [1,4,2,6,7,8,3,5]=>84 [1,4,2,6,3,8,5,7]=>61 [1,4,2,6,3,5,7,8]=>5 [1,4,2,7,3,8,5,6]=>91 [1,4,2,7,3,5,6,8]=>9 [1,4,2,3,7,5,6,8]=>6 [1,4,2,3,5,7,6,8]=>3 [1,4,2,8,3,5,6,7]=>14 [1,4,2,3,5,8,6,7]=>6 [1,4,2,3,5,6,7,8]=>1 [1,5,2,6,3,7,4,8]=>16 [1,5,2,6,3,8,4,7]=>77 [1,5,2,6,3,4,7,8]=>5 [1,2,5,6,3,4,7,8]=>2 [1,5,2,7,3,8,4,6]=>168 [1,5,2,7,3,4,6,8]=>14 [1,5,2,3,4,7,6,8]=>4 [1,5,2,8,3,4,6,7]=>28 [1,5,8,2,3,4,6,7]=>28 [1,5,2,3,4,8,6,7]=>10 [1,2,3,5,4,8,6,7]=>3 [1,5,2,3,4,6,7,8]=>1 [1,6,2,7,3,8,4,5]=>168 [1,6,7,8,2,3,4,5]=>462 [1,6,2,7,3,4,5,8]=>14 [1,6,7,2,3,4,5,8]=>14 [1,6,2,3,4,7,5,8]=>4 [1,2,3,6,4,7,5,8]=>2 [1,6,2,8,3,4,5,7]=>42 [1,6,8,2,3,4,5,7]=>42 [1,6,2,3,4,8,5,7]=>14 [1,2,3,6,4,8,5,7]=>5 [1,6,2,3,4,5,7,8]=>1 [1,2,3,6,4,5,7,8]=>1 [1,7,2,8,3,4,5,6]=>42 [1,7,8,2,3,4,5,6]=>42 [1,7,2,3,8,4,5,6]=>28 [1,7,2,3,4,8,5,6]=>14 [1,2,3,7,4,8,5,6]=>5 [1,7,2,3,4,5,8,6]=>5 [1,2,7,3,4,5,8,6]=>4 [1,7,2,3,4,5,6,8]=>1 [1,2,3,7,4,5,6,8]=>1 [1,2,3,8,4,5,6,7]=>1 [1,2,3,4,5,8,6,7]=>1 [1,6,7,4,5,2,3,8]=>2640 [1,5,4,7,6,2,3,8]=>552 [1,5,3,7,2,6,4,8]=>244 [1,6,7,3,2,5,4,8]=>552 [1,5,6,3,4,8,7,2]=>2090 [1,7,5,4,8,3,6,2]=>474903 [1,7,6,8,4,3,5,2]=>2362932 [1,6,7,8,3,4,5,2]=>50050 [1,5,7,3,8,4,6,2]=>23452 [1,4,3,7,8,5,6,2]=>2090 [1,5,8,3,7,6,4,2]=>474903 [1,6,8,7,3,5,4,2]=>2362932 [1,7,8,6,5,3,4,2]=>26604864 [1,4,6,7,3,2,8,5]=>912 [1,7,4,5,3,2,8,6]=>4675 [1,7,4,8,6,3,5,2]=>1153152 [1,7,3,5,6,8,2,4]=>3520 [1,3,6,7,5,8,2,4]=>990 [1,7,3,4,2,5,8,6]=>99 [1,7,2,5,8,6,4,3]=>21450 [1,7,4,8,2,6,5,3]=>132704 [1,7,2,8,5,3,4,6]=>990 [1,2,8,7,6,3,4,5]=>2112 [1,7,2,3,4,6,5,8]=>5 [1,6,2,5,3,4,7,8]=>9 [1,6,4,7,5,8,2,3]=>8580 [1,3,7,4,6,8,2,5]=>567 [1,7,6,5,4,8,2,3]=>640640 [1,2,7,6,8,3,4,5]=>210 [1,6,2,5,8,3,4,7]=>288 [1,5,4,2,8,3,6,7]=>232 [1,7,6,8,5,4,2,3]=>5105100 [1,4,8,6,7,5,2,3]=>126126 [1,3,8,7,5,6,2,4]=>68640 [1,5,8,4,3,2,6,7]=>2310 [1,7,4,3,8,5,2,6]=>11220 [1,5,7,3,8,4,2,6]=>8613 [1,4,3,8,7,5,6,2]=>11121 [1,6,8,5,3,7,4,2]=>1153152 [1,7,5,6,3,2,8,4]=>27599 [1,6,7,2,8,4,3,5]=>2970 [1,7,2,8,4,5,3,6]=>1155 [1,2,7,5,8,3,4,6]=>168 [1,2,8,7,4,5,6,3]=>3520 [1,7,8,5,2,6,4,3]=>640640 [1,7,2,4,3,5,6,8]=>5 [1,6,2,4,3,5,7,8]=>4 [1,5,2,4,3,6,7,8]=>3 [1,7,2,5,3,4,6,8]=>14 [1,7,2,6,3,4,5,8]=>28 [1,7,2,8,3,5,4,6]=>288 [1,6,2,8,3,5,4,7]=>246 [1,5,2,8,3,6,4,7]=>134 [1,4,2,8,3,6,5,7]=>78 [1,3,2,8,4,6,5,7]=>24 [1,2,3,8,4,6,5,7]=>4 [1,2,3,7,4,6,5,8]=>3 [1,3,2,7,4,6,5,8]=>15 [1,4,2,7,3,6,5,8]=>40 [1,5,2,7,3,6,4,8]=>56 [1,6,2,7,3,5,4,8]=>70 [1,7,2,6,3,5,4,8]=>162 [1,7,2,5,3,6,4,8]=>64 [1,6,2,5,3,7,4,8]=>35 [1,5,2,4,3,7,6,8]=>15 [1,6,2,4,3,7,5,8]=>19 [1,7,2,4,3,6,5,8]=>29 [1,7,2,4,3,8,5,6]=>92 [1,6,2,4,3,8,5,7]=>78 [1,5,2,4,3,8,6,7]=>45 [1,6,2,5,3,8,4,7]=>190 [1,7,2,5,3,8,4,6]=>282 [1,7,2,6,3,8,4,5]=>450 [1,2,3,8,4,7,5,6]=>9 [1,3,2,8,4,7,5,6]=>63 [1,4,2,8,3,7,5,6]=>232 [1,5,2,8,3,7,4,6]=>534 [1,6,2,8,3,7,4,5]=>702 [1,7,2,8,3,6,4,5]=>990 [1,2,3,4,5,6,7,8,9]=>1 [1,2,3,4,5,6,7,9,8]=>1 [1,7,9,2,3,4,5,6,8]=>132 [1,2,3,4,5,6,7,8,9,10]=>1 [1,2,3,4,5,6,7,8,10,9]=>1 [1,2,3,4,5,6,7,8,9,11,10]=>1
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Description
The number of reduced words for a permutation.
This is the number of ways to write a permutation as a minimal length product of simple transpositions. E.g., there are two reduced words for the permutation $[3,2,1]$, which are $(1,2)(2,3)(1,2) = (2,3)(1,2)(2,3)$.
References
[1] Edelman, P., Greene, C. Balanced tableaux MathSciNet:0871081
[2] Number of simple allowable sequences on 1..n containing the permutation 12...n. OEIS:A005118
[3] Total number of reduced decompositions for all permutations in S_n. OEIS:A246865
Code
def statistic(x):
    return sum(1 for _ in x.reduced_words_iterator())

Created
Sep 13, 2011 at 22:02 by Chris Berg
Updated
May 23, 2019 at 16:07 by Martin Rubey