Identifier
- St001482: Permutations ⟶ ℤ
Values
=>
[1]=>1
[1,2]=>1
[2,1]=>2
[1,2,3]=>3
[1,3,2]=>4
[2,1,3]=>6
[2,3,1]=>10
[3,1,2]=>12
[3,2,1]=>15
[1,2,3,4]=>18
[1,2,4,3]=>21
[1,3,2,4]=>24
[1,3,4,2]=>32
[1,4,2,3]=>35
[1,4,3,2]=>40
[2,1,3,4]=>36
[2,1,4,3]=>42
[2,3,1,4]=>60
[2,3,4,1]=>90
[2,4,1,3]=>84
[2,4,3,1]=>108
[3,1,2,4]=>72
[3,1,4,2]=>96
[3,2,1,4]=>90
[3,2,4,1]=>135
[3,4,1,2]=>168
[3,4,2,1]=>189
[4,1,2,3]=>140
[4,1,3,2]=>160
[4,2,1,3]=>168
[4,2,3,1]=>216
[4,3,1,2]=>224
[4,3,2,1]=>252
[1,2,3,4,5]=>180
[1,2,3,5,4]=>198
[1,2,4,3,5]=>210
[1,2,4,5,3]=>252
[1,2,5,3,4]=>264
[1,2,5,4,3]=>288
[1,3,2,4,5]=>240
[1,3,2,5,4]=>264
[1,3,4,2,5]=>320
[1,3,4,5,2]=>416
[1,3,5,2,4]=>396
[1,3,5,4,2]=>468
[1,4,2,3,5]=>350
[1,4,2,5,3]=>420
[1,4,3,2,5]=>400
[1,4,3,5,2]=>520
[1,4,5,2,3]=>600
[1,4,5,3,2]=>650
[1,5,2,3,4]=>528
[1,5,2,4,3]=>576
[1,5,3,2,4]=>594
[1,5,3,4,2]=>702
[1,5,4,2,3]=>720
[1,5,4,3,2]=>780
[2,1,3,4,5]=>360
[2,1,3,5,4]=>396
[2,1,4,3,5]=>420
[2,1,4,5,3]=>504
[2,1,5,3,4]=>528
[2,1,5,4,3]=>576
[2,3,1,4,5]=>600
[2,3,1,5,4]=>660
[2,3,4,1,5]=>900
[2,3,4,5,1]=>1260
[2,3,5,1,4]=>1100
[2,3,5,4,1]=>1400
[2,4,1,3,5]=>840
[2,4,1,5,3]=>1008
[2,4,3,1,5]=>1080
[2,4,3,5,1]=>1512
[2,4,5,1,3]=>1584
[2,4,5,3,1]=>1848
[2,5,1,3,4]=>1232
[2,5,1,4,3]=>1344
[2,5,3,1,4]=>1540
[2,5,3,4,1]=>1960
[2,5,4,1,3]=>1848
[2,5,4,3,1]=>2156
[3,1,2,4,5]=>720
[3,1,2,5,4]=>792
[3,1,4,2,5]=>960
[3,1,4,5,2]=>1248
[3,1,5,2,4]=>1188
[3,1,5,4,2]=>1404
[3,2,1,4,5]=>900
[3,2,1,5,4]=>990
[3,2,4,1,5]=>1350
[3,2,4,5,1]=>1890
[3,2,5,1,4]=>1650
[3,2,5,4,1]=>2100
[3,4,1,2,5]=>1680
[3,4,1,5,2]=>2184
[3,4,2,1,5]=>1890
[3,4,2,5,1]=>2646
[3,4,5,1,2]=>3276
[3,4,5,2,1]=>3528
[3,5,1,2,4]=>2376
[3,5,1,4,2]=>2808
[3,5,2,1,4]=>2640
[3,5,2,4,1]=>3360
[3,5,4,1,2]=>3744
[3,5,4,2,1]=>4032
[4,1,2,3,5]=>1400
[4,1,2,5,3]=>1680
[4,1,3,2,5]=>1600
[4,1,3,5,2]=>2080
[4,1,5,2,3]=>2400
[4,1,5,3,2]=>2600
[4,2,1,3,5]=>1680
[4,2,1,5,3]=>2016
[4,2,3,1,5]=>2160
[4,2,3,5,1]=>3024
[4,2,5,1,3]=>3168
[4,2,5,3,1]=>3696
[4,3,1,2,5]=>2240
[4,3,1,5,2]=>2912
[4,3,2,1,5]=>2520
[4,3,2,5,1]=>3528
[4,3,5,1,2]=>4368
[4,3,5,2,1]=>4704
[4,5,1,2,3]=>4320
[4,5,1,3,2]=>4680
[4,5,2,1,3]=>4752
[4,5,2,3,1]=>5544
[4,5,3,1,2]=>5616
[4,5,3,2,1]=>6048
[5,1,2,3,4]=>2640
[5,1,2,4,3]=>2880
[5,1,3,2,4]=>2970
[5,1,3,4,2]=>3510
[5,1,4,2,3]=>3600
[5,1,4,3,2]=>3900
[5,2,1,3,4]=>3080
[5,2,1,4,3]=>3360
[5,2,3,1,4]=>3850
[5,2,3,4,1]=>4900
[5,2,4,1,3]=>4620
[5,2,4,3,1]=>5390
[5,3,1,2,4]=>3960
[5,3,1,4,2]=>4680
[5,3,2,1,4]=>4400
[5,3,2,4,1]=>5600
[5,3,4,1,2]=>6240
[5,3,4,2,1]=>6720
[5,4,1,2,3]=>5400
[5,4,1,3,2]=>5850
[5,4,2,1,3]=>5940
[5,4,2,3,1]=>6930
[5,4,3,1,2]=>7020
[5,4,3,2,1]=>7560
[1,2,3,4,5,6]=>2700
[1,2,3,4,6,5]=>2880
[1,2,3,5,4,6]=>2970
[1,2,3,5,6,4]=>3366
[1,2,3,6,4,5]=>3456
[1,2,3,6,5,4]=>3672
[1,2,4,3,5,6]=>3150
[1,2,4,3,6,5]=>3360
[1,2,4,5,3,6]=>3780
[1,2,4,5,6,3]=>4536
[1,2,4,6,3,5]=>4368
[1,2,4,6,5,3]=>4914
[1,2,5,3,4,6]=>3960
[1,2,5,3,6,4]=>4488
[1,2,5,4,3,6]=>4320
[1,2,5,4,6,3]=>5184
[1,2,5,6,3,4]=>5712
[1,2,5,6,4,3]=>6048
[1,2,6,3,4,5]=>5184
[1,2,6,3,5,4]=>5508
[1,2,6,4,3,5]=>5616
[1,2,6,4,5,3]=>6318
[1,2,6,5,3,4]=>6426
[1,2,6,5,4,3]=>6804
[1,3,2,4,5,6]=>3600
[1,3,2,4,6,5]=>3840
[1,3,2,5,4,6]=>3960
[1,3,2,5,6,4]=>4488
[1,3,2,6,4,5]=>4608
[1,3,2,6,5,4]=>4896
[1,3,4,2,5,6]=>4800
[1,3,4,2,6,5]=>5120
[1,3,4,5,2,6]=>6240
[1,3,4,5,6,2]=>7904
[1,3,4,6,2,5]=>7168
[1,3,4,6,5,2]=>8512
[1,3,5,2,4,6]=>5940
[1,3,5,2,6,4]=>6732
[1,3,5,4,2,6]=>7020
[1,3,5,4,6,2]=>8892
[1,3,5,6,2,4]=>9180
[1,3,5,6,4,2]=>10260
[1,3,6,2,4,5]=>7680
[1,3,6,2,5,4]=>8160
[1,3,6,4,2,5]=>8960
[1,3,6,4,5,2]=>10640
[1,3,6,5,2,4]=>10200
[1,3,6,5,4,2]=>11400
[1,4,2,3,5,6]=>5250
[1,4,2,3,6,5]=>5600
[1,4,2,5,3,6]=>6300
[1,4,2,5,6,3]=>7560
[1,4,2,6,3,5]=>7280
[1,4,2,6,5,3]=>8190
[1,4,3,2,5,6]=>6000
[1,4,3,2,6,5]=>6400
[1,4,3,5,2,6]=>7800
[1,4,3,5,6,2]=>9880
[1,4,3,6,2,5]=>8960
[1,4,3,6,5,2]=>10640
[1,4,5,2,3,6]=>9000
[1,4,5,2,6,3]=>10800
[1,4,5,3,2,6]=>9750
[1,4,5,3,6,2]=>12350
[1,4,5,6,2,3]=>14400
[1,4,5,6,3,2]=>15200
[1,4,6,2,3,5]=>11440
[1,4,6,2,5,3]=>12870
[1,4,6,3,2,5]=>12320
[1,4,6,3,5,2]=>14630
[1,4,6,5,2,3]=>15840
[1,4,6,5,3,2]=>16720
[1,5,2,3,4,6]=>7920
[1,5,2,3,6,4]=>8976
[1,5,2,4,3,6]=>8640
[1,5,2,4,6,3]=>10368
[1,5,2,6,3,4]=>11424
[1,5,2,6,4,3]=>12096
[1,5,3,2,4,6]=>8910
[1,5,3,2,6,4]=>10098
[1,5,3,4,2,6]=>10530
[1,5,3,4,6,2]=>13338
[1,5,3,6,2,4]=>13770
[1,5,3,6,4,2]=>15390
[1,5,4,2,3,6]=>10800
[1,5,4,2,6,3]=>12960
[1,5,4,3,2,6]=>11700
[1,5,4,3,6,2]=>14820
[1,5,4,6,2,3]=>17280
[1,5,4,6,3,2]=>18240
[1,5,6,2,3,4]=>17136
[1,5,6,2,4,3]=>18144
[1,5,6,3,2,4]=>18360
[1,5,6,3,4,2]=>20520
[1,5,6,4,2,3]=>20736
[1,5,6,4,3,2]=>21888
[1,6,2,3,4,5]=>12096
[1,6,2,3,5,4]=>12852
[1,6,2,4,3,5]=>13104
[1,6,2,4,5,3]=>14742
[1,6,2,5,3,4]=>14994
[1,6,2,5,4,3]=>15876
[1,6,3,2,4,5]=>13440
[1,6,3,2,5,4]=>14280
[1,6,3,4,2,5]=>15680
[1,6,3,4,5,2]=>18620
[1,6,3,5,2,4]=>17850
[1,6,3,5,4,2]=>19950
[1,6,4,2,3,5]=>16016
[1,6,4,2,5,3]=>18018
[1,6,4,3,2,5]=>17248
[1,6,4,3,5,2]=>20482
[1,6,4,5,2,3]=>22176
[1,6,4,5,3,2]=>23408
[1,6,5,2,3,4]=>19992
[1,6,5,2,4,3]=>21168
[1,6,5,3,2,4]=>21420
[1,6,5,3,4,2]=>23940
[1,6,5,4,2,3]=>24192
[1,6,5,4,3,2]=>25536
[2,1,3,4,5,6]=>5400
[2,1,3,4,6,5]=>5760
[2,1,3,5,4,6]=>5940
[2,1,3,5,6,4]=>6732
[2,1,3,6,4,5]=>6912
[2,1,3,6,5,4]=>7344
[2,1,4,3,5,6]=>6300
[2,1,4,3,6,5]=>6720
[2,1,4,5,3,6]=>7560
[2,1,4,5,6,3]=>9072
[2,1,4,6,3,5]=>8736
[2,1,4,6,5,3]=>9828
[2,1,5,3,4,6]=>7920
[2,1,5,3,6,4]=>8976
[2,1,5,4,3,6]=>8640
[2,1,5,4,6,3]=>10368
[2,1,5,6,3,4]=>11424
[2,1,5,6,4,3]=>12096
[2,1,6,3,4,5]=>10368
[2,1,6,3,5,4]=>11016
[2,1,6,4,3,5]=>11232
[2,1,6,4,5,3]=>12636
[2,1,6,5,3,4]=>12852
[2,1,6,5,4,3]=>13608
[2,3,1,4,5,6]=>9000
[2,3,1,4,6,5]=>9600
[2,3,1,5,4,6]=>9900
[2,3,1,5,6,4]=>11220
[2,3,1,6,4,5]=>11520
[2,3,1,6,5,4]=>12240
[2,3,4,1,5,6]=>13500
[2,3,4,1,6,5]=>14400
[2,3,4,5,1,6]=>18900
[2,3,4,5,6,1]=>25200
[2,3,4,6,1,5]=>21600
[2,3,4,6,5,1]=>27000
[2,3,5,1,4,6]=>16500
[2,3,5,1,6,4]=>18700
[2,3,5,4,1,6]=>21000
[2,3,5,4,6,1]=>28000
[2,3,5,6,1,4]=>27200
[2,3,5,6,4,1]=>32000
[2,3,6,1,4,5]=>21120
[2,3,6,1,5,4]=>22440
[2,3,6,4,1,5]=>26400
[2,3,6,4,5,1]=>33000
[2,3,6,5,1,4]=>29920
[2,3,6,5,4,1]=>35200
[2,4,1,3,5,6]=>12600
[2,4,1,3,6,5]=>13440
[2,4,1,5,3,6]=>15120
[2,4,1,5,6,3]=>18144
[2,4,1,6,3,5]=>17472
[2,4,1,6,5,3]=>19656
[2,4,3,1,5,6]=>16200
[2,4,3,1,6,5]=>17280
[2,4,3,5,1,6]=>22680
[2,4,3,5,6,1]=>30240
[2,4,3,6,1,5]=>25920
[2,4,3,6,5,1]=>32400
[2,4,5,1,3,6]=>23760
[2,4,5,1,6,3]=>28512
[2,4,5,3,1,6]=>27720
[2,4,5,3,6,1]=>36960
[2,4,5,6,1,3]=>40392
[2,4,5,6,3,1]=>44880
[2,4,6,1,3,5]=>29952
[2,4,6,1,5,3]=>33696
[2,4,6,3,1,5]=>34560
[2,4,6,3,5,1]=>43200
[2,4,6,5,1,3]=>44064
[2,4,6,5,3,1]=>48960
[2,5,1,3,4,6]=>18480
[2,5,1,3,6,4]=>20944
[2,5,1,4,3,6]=>20160
[2,5,1,4,6,3]=>24192
[2,5,1,6,3,4]=>26656
[2,5,1,6,4,3]=>28224
[2,5,3,1,4,6]=>23100
[2,5,3,1,6,4]=>26180
[2,5,3,4,1,6]=>29400
[2,5,3,4,6,1]=>39200
[2,5,3,6,1,4]=>38080
[2,5,3,6,4,1]=>44800
[2,5,4,1,3,6]=>27720
[2,5,4,1,6,3]=>33264
[2,5,4,3,1,6]=>32340
[2,5,4,3,6,1]=>43120
[2,5,4,6,1,3]=>47124
[2,5,4,6,3,1]=>52360
[2,5,6,1,3,4]=>43316
[2,5,6,1,4,3]=>45864
[2,5,6,3,1,4]=>49504
[2,5,6,3,4,1]=>58240
[2,5,6,4,1,3]=>55692
[2,5,6,4,3,1]=>61880
[2,6,1,3,4,5]=>27648
[2,6,1,3,5,4]=>29376
[2,6,1,4,3,5]=>29952
[2,6,1,4,5,3]=>33696
[2,6,1,5,3,4]=>34272
[2,6,1,5,4,3]=>36288
[2,6,3,1,4,5]=>33792
[2,6,3,1,5,4]=>35904
[2,6,3,4,1,5]=>42240
[2,6,3,4,5,1]=>52800
[2,6,3,5,1,4]=>47872
[2,6,3,5,4,1]=>56320
[2,6,4,1,3,5]=>39936
[2,6,4,1,5,3]=>44928
[2,6,4,3,1,5]=>46080
[2,6,4,3,5,1]=>57600
[2,6,4,5,1,3]=>58752
[2,6,4,5,3,1]=>65280
[2,6,5,1,3,4]=>49504
[2,6,5,1,4,3]=>52416
[2,6,5,3,1,4]=>56576
[2,6,5,3,4,1]=>66560
[2,6,5,4,1,3]=>63648
[2,6,5,4,3,1]=>70720
[3,1,2,4,5,6]=>10800
[3,1,2,4,6,5]=>11520
[3,1,2,5,4,6]=>11880
[3,1,2,5,6,4]=>13464
[3,1,2,6,4,5]=>13824
[3,1,2,6,5,4]=>14688
[3,1,4,2,5,6]=>14400
[3,1,4,2,6,5]=>15360
[3,1,4,5,2,6]=>18720
[3,1,4,5,6,2]=>23712
[3,1,4,6,2,5]=>21504
[3,1,4,6,5,2]=>25536
[3,1,5,2,4,6]=>17820
[3,1,5,2,6,4]=>20196
[3,1,5,4,2,6]=>21060
[3,1,5,4,6,2]=>26676
[3,1,5,6,2,4]=>27540
[3,1,5,6,4,2]=>30780
[3,1,6,2,4,5]=>23040
[3,1,6,2,5,4]=>24480
[3,1,6,4,2,5]=>26880
[3,1,6,4,5,2]=>31920
[3,1,6,5,2,4]=>30600
[3,1,6,5,4,2]=>34200
[3,2,1,4,5,6]=>13500
[3,2,1,4,6,5]=>14400
[3,2,1,5,4,6]=>14850
[3,2,1,5,6,4]=>16830
[3,2,1,6,4,5]=>17280
[3,2,1,6,5,4]=>18360
[3,2,4,1,5,6]=>20250
[3,2,4,1,6,5]=>21600
[3,2,4,5,1,6]=>28350
[3,2,4,5,6,1]=>37800
[3,2,4,6,1,5]=>32400
[3,2,4,6,5,1]=>40500
[3,2,5,1,4,6]=>24750
[3,2,5,1,6,4]=>28050
[3,2,5,4,1,6]=>31500
[3,2,5,4,6,1]=>42000
[3,2,5,6,1,4]=>40800
[3,2,5,6,4,1]=>48000
[3,2,6,1,4,5]=>31680
[3,2,6,1,5,4]=>33660
[3,2,6,4,1,5]=>39600
[3,2,6,4,5,1]=>49500
[3,2,6,5,1,4]=>44880
[3,2,6,5,4,1]=>52800
[3,4,1,2,5,6]=>25200
[3,4,1,2,6,5]=>26880
[3,4,1,5,2,6]=>32760
[3,4,1,5,6,2]=>41496
[3,4,1,6,2,5]=>37632
[3,4,1,6,5,2]=>44688
[3,4,2,1,5,6]=>28350
[3,4,2,1,6,5]=>30240
[3,4,2,5,1,6]=>39690
[3,4,2,5,6,1]=>52920
[3,4,2,6,1,5]=>45360
[3,4,2,6,5,1]=>56700
[3,4,5,1,2,6]=>49140
[3,4,5,1,6,2]=>62244
[3,4,5,2,1,6]=>52920
[3,4,5,2,6,1]=>70560
[3,4,5,6,1,2]=>86184
[3,4,5,6,2,1]=>90720
[3,4,6,1,2,5]=>61152
[3,4,6,1,5,2]=>72618
[3,4,6,2,1,5]=>65520
[3,4,6,2,5,1]=>81900
[3,4,6,5,1,2]=>93366
[3,4,6,5,2,1]=>98280
[3,5,1,2,4,6]=>35640
[3,5,1,2,6,4]=>40392
[3,5,1,4,2,6]=>42120
[3,5,1,4,6,2]=>53352
[3,5,1,6,2,4]=>55080
[3,5,1,6,4,2]=>61560
[3,5,2,1,4,6]=>39600
[3,5,2,1,6,4]=>44880
[3,5,2,4,1,6]=>50400
[3,5,2,4,6,1]=>67200
[3,5,2,6,1,4]=>65280
[3,5,2,6,4,1]=>76800
[3,5,4,1,2,6]=>56160
[3,5,4,1,6,2]=>71136
[3,5,4,2,1,6]=>60480
[3,5,4,2,6,1]=>80640
[3,5,4,6,1,2]=>98496
[3,5,4,6,2,1]=>103680
[3,5,6,1,2,4]=>85680
[3,5,6,1,4,2]=>95760
[3,5,6,2,1,4]=>91392
[3,5,6,2,4,1]=>107520
[3,5,6,4,1,2]=>114912
[3,5,6,4,2,1]=>120960
[3,6,1,2,4,5]=>51840
[3,6,1,2,5,4]=>55080
[3,6,1,4,2,5]=>60480
[3,6,1,4,5,2]=>71820
[3,6,1,5,2,4]=>68850
[3,6,1,5,4,2]=>76950
[3,6,2,1,4,5]=>57024
[3,6,2,1,5,4]=>60588
[3,6,2,4,1,5]=>71280
[3,6,2,4,5,1]=>89100
[3,6,2,5,1,4]=>80784
[3,6,2,5,4,1]=>95040
[3,6,4,1,2,5]=>78624
[3,6,4,1,5,2]=>93366
[3,6,4,2,1,5]=>84240
[3,6,4,2,5,1]=>105300
[3,6,4,5,1,2]=>120042
[3,6,4,5,2,1]=>126360
[3,6,5,1,2,4]=>96390
[3,6,5,1,4,2]=>107730
[3,6,5,2,1,4]=>102816
[3,6,5,2,4,1]=>120960
[3,6,5,4,1,2]=>129276
[3,6,5,4,2,1]=>136080
[4,1,2,3,5,6]=>21000
[4,1,2,3,6,5]=>22400
[4,1,2,5,3,6]=>25200
[4,1,2,5,6,3]=>30240
[4,1,2,6,3,5]=>29120
[4,1,2,6,5,3]=>32760
[4,1,3,2,5,6]=>24000
[4,1,3,2,6,5]=>25600
[4,1,3,5,2,6]=>31200
[4,1,3,5,6,2]=>39520
[4,1,3,6,2,5]=>35840
[4,1,3,6,5,2]=>42560
[4,1,5,2,3,6]=>36000
[4,1,5,2,6,3]=>43200
[4,1,5,3,2,6]=>39000
[4,1,5,3,6,2]=>49400
[4,1,5,6,2,3]=>57600
[4,1,5,6,3,2]=>60800
[4,1,6,2,3,5]=>45760
[4,1,6,2,5,3]=>51480
[4,1,6,3,2,5]=>49280
[4,1,6,3,5,2]=>58520
[4,1,6,5,2,3]=>63360
[4,1,6,5,3,2]=>66880
[4,2,1,3,5,6]=>25200
[4,2,1,3,6,5]=>26880
[4,2,1,5,3,6]=>30240
[4,2,1,5,6,3]=>36288
[4,2,1,6,3,5]=>34944
[4,2,1,6,5,3]=>39312
[4,2,3,1,5,6]=>32400
[4,2,3,1,6,5]=>34560
[4,2,3,5,1,6]=>45360
[4,2,3,5,6,1]=>60480
[4,2,3,6,1,5]=>51840
[4,2,3,6,5,1]=>64800
[4,2,5,1,3,6]=>47520
[4,2,5,1,6,3]=>57024
[4,2,5,3,1,6]=>55440
[4,2,5,3,6,1]=>73920
[4,2,5,6,1,3]=>80784
[4,2,5,6,3,1]=>89760
[4,2,6,1,3,5]=>59904
[4,2,6,1,5,3]=>67392
[4,2,6,3,1,5]=>69120
[4,2,6,3,5,1]=>86400
[4,2,6,5,1,3]=>88128
[4,2,6,5,3,1]=>97920
[4,3,1,2,5,6]=>33600
[4,3,1,2,6,5]=>35840
[4,3,1,5,2,6]=>43680
[4,3,1,5,6,2]=>55328
[4,3,1,6,2,5]=>50176
[4,3,1,6,5,2]=>59584
[4,3,2,1,5,6]=>37800
[4,3,2,1,6,5]=>40320
[4,3,2,5,1,6]=>52920
[4,3,2,5,6,1]=>70560
[4,3,2,6,1,5]=>60480
[4,3,2,6,5,1]=>75600
[4,3,5,1,2,6]=>65520
[4,3,5,1,6,2]=>82992
[4,3,5,2,1,6]=>70560
[4,3,5,2,6,1]=>94080
[4,3,5,6,1,2]=>114912
[4,3,5,6,2,1]=>120960
[4,3,6,1,2,5]=>81536
[4,3,6,1,5,2]=>96824
[4,3,6,2,1,5]=>87360
[4,3,6,2,5,1]=>109200
[4,3,6,5,1,2]=>124488
[4,3,6,5,2,1]=>131040
[4,5,1,2,3,6]=>64800
[4,5,1,2,6,3]=>77760
[4,5,1,3,2,6]=>70200
[4,5,1,3,6,2]=>88920
[4,5,1,6,2,3]=>103680
[4,5,1,6,3,2]=>109440
[4,5,2,1,3,6]=>71280
[4,5,2,1,6,3]=>85536
[4,5,2,3,1,6]=>83160
[4,5,2,3,6,1]=>110880
[4,5,2,6,1,3]=>121176
[4,5,2,6,3,1]=>134640
[4,5,3,1,2,6]=>84240
[4,5,3,1,6,2]=>106704
[4,5,3,2,1,6]=>90720
[4,5,3,2,6,1]=>120960
[4,5,3,6,1,2]=>147744
[4,5,3,6,2,1]=>155520
[4,5,6,1,2,3]=>155520
[4,5,6,1,3,2]=>164160
[4,5,6,2,1,3]=>165240
[4,5,6,2,3,1]=>183600
[4,5,6,3,1,2]=>184680
[4,5,6,3,2,1]=>194400
[4,6,1,2,3,5]=>91520
[4,6,1,2,5,3]=>102960
[4,6,1,3,2,5]=>98560
[4,6,1,3,5,2]=>117040
[4,6,1,5,2,3]=>126720
[4,6,1,5,3,2]=>133760
[4,6,2,1,3,5]=>99840
[4,6,2,1,5,3]=>112320
[4,6,2,3,1,5]=>115200
[4,6,2,3,5,1]=>144000
[4,6,2,5,1,3]=>146880
[4,6,2,5,3,1]=>163200
[4,6,3,1,2,5]=>116480
[4,6,3,1,5,2]=>138320
[4,6,3,2,1,5]=>124800
[4,6,3,2,5,1]=>156000
[4,6,3,5,1,2]=>177840
[4,6,3,5,2,1]=>187200
[4,6,5,1,2,3]=>172800
[4,6,5,1,3,2]=>182400
[4,6,5,2,1,3]=>183600
[4,6,5,2,3,1]=>204000
[4,6,5,3,1,2]=>205200
[4,6,5,3,2,1]=>216000
[5,1,2,3,4,6]=>39600
[5,1,2,3,6,4]=>44880
[5,1,2,4,3,6]=>43200
[5,1,2,4,6,3]=>51840
[5,1,2,6,3,4]=>57120
[5,1,2,6,4,3]=>60480
[5,1,3,2,4,6]=>44550
[5,1,3,2,6,4]=>50490
[5,1,3,4,2,6]=>52650
[5,1,3,4,6,2]=>66690
[5,1,3,6,2,4]=>68850
[5,1,3,6,4,2]=>76950
[5,1,4,2,3,6]=>54000
[5,1,4,2,6,3]=>64800
[5,1,4,3,2,6]=>58500
[5,1,4,3,6,2]=>74100
[5,1,4,6,2,3]=>86400
[5,1,4,6,3,2]=>91200
[5,1,6,2,3,4]=>85680
[5,1,6,2,4,3]=>90720
[5,1,6,3,2,4]=>91800
[5,1,6,3,4,2]=>102600
[5,1,6,4,2,3]=>103680
[5,1,6,4,3,2]=>109440
[5,2,1,3,4,6]=>46200
[5,2,1,3,6,4]=>52360
[5,2,1,4,3,6]=>50400
[5,2,1,4,6,3]=>60480
[5,2,1,6,3,4]=>66640
[5,2,1,6,4,3]=>70560
[5,2,3,1,4,6]=>57750
[5,2,3,1,6,4]=>65450
[5,2,3,4,1,6]=>73500
[5,2,3,4,6,1]=>98000
[5,2,3,6,1,4]=>95200
[5,2,3,6,4,1]=>112000
[5,2,4,1,3,6]=>69300
[5,2,4,1,6,3]=>83160
[5,2,4,3,1,6]=>80850
[5,2,4,3,6,1]=>107800
[5,2,4,6,1,3]=>117810
[5,2,4,6,3,1]=>130900
[5,2,6,1,3,4]=>108290
[5,2,6,1,4,3]=>114660
[5,2,6,3,1,4]=>123760
[5,2,6,3,4,1]=>145600
[5,2,6,4,1,3]=>139230
[5,2,6,4,3,1]=>154700
[5,3,1,2,4,6]=>59400
[5,3,1,2,6,4]=>67320
[5,3,1,4,2,6]=>70200
[5,3,1,4,6,2]=>88920
[5,3,1,6,2,4]=>91800
[5,3,1,6,4,2]=>102600
[5,3,2,1,4,6]=>66000
[5,3,2,1,6,4]=>74800
[5,3,2,4,1,6]=>84000
[5,3,2,4,6,1]=>112000
[5,3,2,6,1,4]=>108800
[5,3,2,6,4,1]=>128000
[5,3,4,1,2,6]=>93600
[5,3,4,1,6,2]=>118560
[5,3,4,2,1,6]=>100800
[5,3,4,2,6,1]=>134400
[5,3,4,6,1,2]=>164160
[5,3,4,6,2,1]=>172800
[5,3,6,1,2,4]=>142800
[5,3,6,1,4,2]=>159600
[5,3,6,2,1,4]=>152320
[5,3,6,2,4,1]=>179200
[5,3,6,4,1,2]=>191520
[5,3,6,4,2,1]=>201600
[5,4,1,2,3,6]=>81000
[5,4,1,2,6,3]=>97200
[5,4,1,3,2,6]=>87750
[5,4,1,3,6,2]=>111150
[5,4,1,6,2,3]=>129600
[5,4,1,6,3,2]=>136800
[5,4,2,1,3,6]=>89100
[5,4,2,1,6,3]=>106920
[5,4,2,3,1,6]=>103950
[5,4,2,3,6,1]=>138600
[5,4,2,6,1,3]=>151470
[5,4,2,6,3,1]=>168300
[5,4,3,1,2,6]=>105300
[5,4,3,1,6,2]=>133380
[5,4,3,2,1,6]=>113400
[5,4,3,2,6,1]=>151200
[5,4,3,6,1,2]=>184680
[5,4,3,6,2,1]=>194400
[5,4,6,1,2,3]=>194400
[5,4,6,1,3,2]=>205200
[5,4,6,2,1,3]=>206550
[5,4,6,2,3,1]=>229500
[5,4,6,3,1,2]=>230850
[5,4,6,3,2,1]=>243000
[5,6,1,2,3,4]=>157080
[5,6,1,2,4,3]=>166320
[5,6,1,3,2,4]=>168300
[5,6,1,3,4,2]=>188100
[5,6,1,4,2,3]=>190080
[5,6,1,4,3,2]=>200640
[5,6,2,1,3,4]=>170170
[5,6,2,1,4,3]=>180180
[5,6,2,3,1,4]=>194480
[5,6,2,3,4,1]=>228800
[5,6,2,4,1,3]=>218790
[5,6,2,4,3,1]=>243100
[5,6,3,1,2,4]=>196350
[5,6,3,1,4,2]=>219450
[5,6,3,2,1,4]=>209440
[5,6,3,2,4,1]=>246400
[5,6,3,4,1,2]=>263340
[5,6,3,4,2,1]=>277200
[5,6,4,1,2,3]=>237600
[5,6,4,1,3,2]=>250800
[5,6,4,2,1,3]=>252450
[5,6,4,2,3,1]=>280500
[5,6,4,3,1,2]=>282150
[5,6,4,3,2,1]=>297000
[6,1,2,3,4,5]=>72576
[6,1,2,3,5,4]=>77112
[6,1,2,4,3,5]=>78624
[6,1,2,4,5,3]=>88452
[6,1,2,5,3,4]=>89964
[6,1,2,5,4,3]=>95256
[6,1,3,2,4,5]=>80640
[6,1,3,2,5,4]=>85680
[6,1,3,4,2,5]=>94080
[6,1,3,4,5,2]=>111720
[6,1,3,5,2,4]=>107100
[6,1,3,5,4,2]=>119700
[6,1,4,2,3,5]=>96096
[6,1,4,2,5,3]=>108108
[6,1,4,3,2,5]=>103488
[6,1,4,3,5,2]=>122892
[6,1,4,5,2,3]=>133056
[6,1,4,5,3,2]=>140448
[6,1,5,2,3,4]=>119952
[6,1,5,2,4,3]=>127008
[6,1,5,3,2,4]=>128520
[6,1,5,3,4,2]=>143640
[6,1,5,4,2,3]=>145152
[6,1,5,4,3,2]=>153216
[6,2,1,3,4,5]=>82944
[6,2,1,3,5,4]=>88128
[6,2,1,4,3,5]=>89856
[6,2,1,4,5,3]=>101088
[6,2,1,5,3,4]=>102816
[6,2,1,5,4,3]=>108864
[6,2,3,1,4,5]=>101376
[6,2,3,1,5,4]=>107712
[6,2,3,4,1,5]=>126720
[6,2,3,4,5,1]=>158400
[6,2,3,5,1,4]=>143616
[6,2,3,5,4,1]=>168960
[6,2,4,1,3,5]=>119808
[6,2,4,1,5,3]=>134784
[6,2,4,3,1,5]=>138240
[6,2,4,3,5,1]=>172800
[6,2,4,5,1,3]=>176256
[6,2,4,5,3,1]=>195840
[6,2,5,1,3,4]=>148512
[6,2,5,1,4,3]=>157248
[6,2,5,3,1,4]=>169728
[6,2,5,3,4,1]=>199680
[6,2,5,4,1,3]=>190944
[6,2,5,4,3,1]=>212160
[6,3,1,2,4,5]=>103680
[6,3,1,2,5,4]=>110160
[6,3,1,4,2,5]=>120960
[6,3,1,4,5,2]=>143640
[6,3,1,5,2,4]=>137700
[6,3,1,5,4,2]=>153900
[6,3,2,1,4,5]=>114048
[6,3,2,1,5,4]=>121176
[6,3,2,4,1,5]=>142560
[6,3,2,4,5,1]=>178200
[6,3,2,5,1,4]=>161568
[6,3,2,5,4,1]=>190080
[6,3,4,1,2,5]=>157248
[6,3,4,1,5,2]=>186732
[6,3,4,2,1,5]=>168480
[6,3,4,2,5,1]=>210600
[6,3,4,5,1,2]=>240084
[6,3,4,5,2,1]=>252720
[6,3,5,1,2,4]=>192780
[6,3,5,1,4,2]=>215460
[6,3,5,2,1,4]=>205632
[6,3,5,2,4,1]=>241920
[6,3,5,4,1,2]=>258552
[6,3,5,4,2,1]=>272160
[6,4,1,2,3,5]=>137280
[6,4,1,2,5,3]=>154440
[6,4,1,3,2,5]=>147840
[6,4,1,3,5,2]=>175560
[6,4,1,5,2,3]=>190080
[6,4,1,5,3,2]=>200640
[6,4,2,1,3,5]=>149760
[6,4,2,1,5,3]=>168480
[6,4,2,3,1,5]=>172800
[6,4,2,3,5,1]=>216000
[6,4,2,5,1,3]=>220320
[6,4,2,5,3,1]=>244800
[6,4,3,1,2,5]=>174720
[6,4,3,1,5,2]=>207480
[6,4,3,2,1,5]=>187200
[6,4,3,2,5,1]=>234000
[6,4,3,5,1,2]=>266760
[6,4,3,5,2,1]=>280800
[6,4,5,1,2,3]=>259200
[6,4,5,1,3,2]=>273600
[6,4,5,2,1,3]=>275400
[6,4,5,2,3,1]=>306000
[6,4,5,3,1,2]=>307800
[6,4,5,3,2,1]=>324000
[6,5,1,2,3,4]=>188496
[6,5,1,2,4,3]=>199584
[6,5,1,3,2,4]=>201960
[6,5,1,3,4,2]=>225720
[6,5,1,4,2,3]=>228096
[6,5,1,4,3,2]=>240768
[6,5,2,1,3,4]=>204204
[6,5,2,1,4,3]=>216216
[6,5,2,3,1,4]=>233376
[6,5,2,3,4,1]=>274560
[6,5,2,4,1,3]=>262548
[6,5,2,4,3,1]=>291720
[6,5,3,1,2,4]=>235620
[6,5,3,1,4,2]=>263340
[6,5,3,2,1,4]=>251328
[6,5,3,2,4,1]=>295680
[6,5,3,4,1,2]=>316008
[6,5,3,4,2,1]=>332640
[6,5,4,1,2,3]=>285120
[6,5,4,1,3,2]=>300960
[6,5,4,2,1,3]=>302940
[6,5,4,2,3,1]=>336600
[6,5,4,3,1,2]=>338580
[6,5,4,3,2,1]=>356400
[1,2,3,4,5,6,7]=>56700
[1,2,3,4,5,7,6]=>59400
[1,2,3,4,6,5,7]=>60480
[1,2,3,4,6,7,5]=>66240
[1,2,3,4,7,5,6]=>67320
[1,2,3,4,7,6,5]=>70380
[1,2,3,5,4,6,7]=>62370
[1,2,3,5,4,7,6]=>65340
[1,2,3,5,6,4,7]=>70686
[1,2,3,5,6,7,4]=>80784
[1,2,3,5,7,4,6]=>78408
[1,2,3,5,7,6,4]=>85536
[1,2,3,6,4,5,7]=>72576
[1,2,3,6,4,7,5]=>79488
[1,2,3,6,5,4,7]=>77112
[1,2,3,6,5,7,4]=>88128
[1,2,3,6,7,4,5]=>94392
[1,2,3,6,7,5,4]=>98496
[1,2,3,7,4,5,6]=>87516
[1,2,3,7,4,6,5]=>91494
[1,2,3,7,5,4,6]=>92664
[1,2,3,7,5,6,4]=>101088
[1,2,3,7,6,4,5]=>102258
[1,2,3,7,6,5,4]=>106704
[1,2,4,3,5,6,7]=>66150
[1,2,4,3,5,7,6]=>69300
[1,2,4,3,6,5,7]=>70560
[1,2,4,3,6,7,5]=>77280
[1,2,4,3,7,5,6]=>78540
[1,2,4,3,7,6,5]=>82110
[1,2,4,5,3,6,7]=>79380
[1,2,4,5,3,7,6]=>83160
[1,2,4,5,6,3,7]=>95256
[1,2,4,5,6,7,3]=>113400
[1,2,4,5,7,3,6]=>105336
[1,2,4,5,7,6,3]=>119700
[1,2,4,6,3,5,7]=>91728
[1,2,4,6,3,7,5]=>100464
[1,2,4,6,5,3,7]=>103194
[1,2,4,6,5,7,3]=>122850
[1,2,4,6,7,3,5]=>125580
[1,2,4,6,7,5,3]=>136500
[1,2,4,7,3,5,6]=>109956
[1,2,4,7,3,6,5]=>114954
[1,2,4,7,5,3,6]=>122892
[1,2,4,7,5,6,3]=>139650
[1,2,4,7,6,3,5]=>135240
[1,2,4,7,6,5,3]=>147000
[1,2,5,3,4,6,7]=>83160
[1,2,5,3,4,7,6]=>87120
[1,2,5,3,6,4,7]=>94248
[1,2,5,3,6,7,4]=>107712
[1,2,5,3,7,4,6]=>104544
[1,2,5,3,7,6,4]=>114048
[1,2,5,4,3,6,7]=>90720
[1,2,5,4,3,7,6]=>95040
[1,2,5,4,6,3,7]=>108864
[1,2,5,4,6,7,3]=>129600
[1,2,5,4,7,3,6]=>120384
[1,2,5,4,7,6,3]=>136800
[1,2,5,6,3,4,7]=>119952
[1,2,5,6,3,7,4]=>137088
[1,2,5,6,4,3,7]=>127008
[1,2,5,6,4,7,3]=>151200
[1,2,5,6,7,3,4]=>169344
[1,2,5,6,7,4,3]=>176400
[1,2,5,7,3,4,6]=>142560
[1,2,5,7,3,6,4]=>155520
[1,2,5,7,4,3,6]=>150480
[1,2,5,7,4,6,3]=>171000
[1,2,5,7,6,3,4]=>181440
[1,2,5,7,6,4,3]=>189000
[1,2,6,3,4,5,7]=>108864
[1,2,6,3,4,7,5]=>119232
[1,2,6,3,5,4,7]=>115668
[1,2,6,3,5,7,4]=>132192
[1,2,6,3,7,4,5]=>141588
[1,2,6,3,7,5,4]=>147744
[1,2,6,4,3,5,7]=>117936
[1,2,6,4,3,7,5]=>129168
[1,2,6,4,5,3,7]=>132678
[1,2,6,4,5,7,3]=>157950
[1,2,6,4,7,3,5]=>161460
[1,2,6,4,7,5,3]=>175500
[1,2,6,5,3,4,7]=>134946
[1,2,6,5,3,7,4]=>154224
[1,2,6,5,4,3,7]=>142884
[1,2,6,5,4,7,3]=>170100
[1,2,6,5,7,3,4]=>190512
[1,2,6,5,7,4,3]=>198450
[1,2,6,7,3,4,5]=>188784
[1,2,6,7,3,5,4]=>196992
[1,2,6,7,4,3,5]=>198720
[1,2,6,7,4,5,3]=>216000
[1,2,6,7,5,3,4]=>217728
[1,2,6,7,5,4,3]=>226800
[1,2,7,3,4,5,6]=>145860
[1,2,7,3,4,6,5]=>152490
[1,2,7,3,5,4,6]=>154440
[1,2,7,3,5,6,4]=>168480
[1,2,7,3,6,4,5]=>170430
[1,2,7,3,6,5,4]=>177840
[1,2,7,4,3,5,6]=>157080
[1,2,7,4,3,6,5]=>164220
[1,2,7,4,5,3,6]=>175560
[1,2,7,4,5,6,3]=>199500
[1,2,7,4,6,3,5]=>193200
[1,2,7,4,6,5,3]=>210000
[1,2,7,5,3,4,6]=>178200
[1,2,7,5,3,6,4]=>194400
[1,2,7,5,4,3,6]=>188100
[1,2,7,5,4,6,3]=>213750
[1,2,7,5,6,3,4]=>226800
[1,2,7,5,6,4,3]=>236250
[1,2,7,6,3,4,5]=>209760
[1,2,7,6,3,5,4]=>218880
[1,2,7,6,4,3,5]=>220800
[1,2,7,6,4,5,3]=>240000
[1,2,7,6,5,3,4]=>241920
[1,2,7,6,5,4,3]=>252000
[1,3,2,4,5,6,7]=>75600
[1,3,2,4,5,7,6]=>79200
[1,3,2,4,6,5,7]=>80640
[1,3,2,4,6,7,5]=>88320
[1,3,2,4,7,5,6]=>89760
[1,3,2,4,7,6,5]=>93840
[1,3,2,5,4,6,7]=>83160
[1,3,2,5,4,7,6]=>87120
[1,3,2,5,6,4,7]=>94248
[1,3,2,5,6,7,4]=>107712
[1,3,2,5,7,4,6]=>104544
[1,3,2,5,7,6,4]=>114048
[1,3,2,6,4,5,7]=>96768
[1,3,2,6,4,7,5]=>105984
[1,3,2,6,5,4,7]=>102816
[1,3,2,6,5,7,4]=>117504
[1,3,2,6,7,4,5]=>125856
[1,3,2,6,7,5,4]=>131328
[1,3,2,7,4,5,6]=>116688
[1,3,2,7,4,6,5]=>121992
[1,3,2,7,5,4,6]=>123552
[1,3,2,7,5,6,4]=>134784
[1,3,2,7,6,4,5]=>136344
[1,3,2,7,6,5,4]=>142272
[1,3,4,2,5,6,7]=>100800
[1,3,4,2,5,7,6]=>105600
[1,3,4,2,6,5,7]=>107520
[1,3,4,2,6,7,5]=>117760
[1,3,4,2,7,5,6]=>119680
[1,3,4,2,7,6,5]=>125120
[1,3,4,5,2,6,7]=>131040
[1,3,4,5,2,7,6]=>137280
[1,3,4,5,6,2,7]=>165984
[1,3,4,5,6,7,2]=>205504
[1,3,4,5,7,2,6]=>183040
[1,3,4,5,7,6,2]=>216320
[1,3,4,6,2,5,7]=>150528
[1,3,4,6,2,7,5]=>164864
[1,3,4,6,5,2,7]=>178752
[1,3,4,6,5,7,2]=>221312
[1,3,4,6,7,2,5]=>216384
[1,3,4,6,7,5,2]=>244608
[1,3,4,7,2,5,6]=>179520
[1,3,4,7,2,6,5]=>187680
[1,3,4,7,5,2,6]=>211200
[1,3,4,7,5,6,2]=>249600
[1,3,4,7,6,2,5]=>231840
[1,3,4,7,6,5,2]=>262080
[1,3,5,2,4,6,7]=>124740
[1,3,5,2,4,7,6]=>130680
[1,3,5,2,6,4,7]=>141372
[1,3,5,2,6,7,4]=>161568
[1,3,5,2,7,4,6]=>156816
[1,3,5,2,7,6,4]=>171072
[1,3,5,4,2,6,7]=>147420
[1,3,5,4,2,7,6]=>154440
[1,3,5,4,6,2,7]=>186732
[1,3,5,4,6,7,2]=>231192
[1,3,5,4,7,2,6]=>205920
[1,3,5,4,7,6,2]=>243360
[1,3,5,6,2,4,7]=>192780
[1,3,5,6,2,7,4]=>220320
[1,3,5,6,4,2,7]=>215460
[1,3,5,6,4,7,2]=>266760
[1,3,5,6,7,2,4]=>285120
[1,3,5,6,7,4,2]=>308880
[1,3,5,7,2,4,6]=>228096
[1,3,5,7,2,6,4]=>248832
[1,3,5,7,4,2,6]=>253440
[1,3,5,7,4,6,2]=>299520
[1,3,5,7,6,2,4]=>304128
[1,3,5,7,6,4,2]=>329472
[1,3,6,2,4,5,7]=>161280
[1,3,6,2,4,7,5]=>176640
[1,3,6,2,5,4,7]=>171360
[1,3,6,2,5,7,4]=>195840
[1,3,6,2,7,4,5]=>209760
[1,3,6,2,7,5,4]=>218880
[1,3,6,4,2,5,7]=>188160
[1,3,6,4,2,7,5]=>206080
[1,3,6,4,5,2,7]=>223440
[1,3,6,4,5,7,2]=>276640
[1,3,6,4,7,2,5]=>270480
[1,3,6,4,7,5,2]=>305760
[1,3,6,5,2,4,7]=>214200
[1,3,6,5,2,7,4]=>244800
[1,3,6,5,4,2,7]=>239400
[1,3,6,5,4,7,2]=>296400
[1,3,6,5,7,2,4]=>316800
[1,3,6,5,7,4,2]=>343200
[1,3,6,7,2,4,5]=>297160
[1,3,6,7,2,5,4]=>310080
[1,3,6,7,4,2,5]=>328440
[1,3,6,7,4,5,2]=>371280
[1,3,6,7,5,2,4]=>359040
[1,3,6,7,5,4,2]=>388960
[1,3,7,2,4,5,6]=>213928
[1,3,7,2,4,6,5]=>223652
[1,3,7,2,5,4,6]=>226512
[1,3,7,2,5,6,4]=>247104
[1,3,7,2,6,4,5]=>249964
[1,3,7,2,6,5,4]=>260832
[1,3,7,4,2,5,6]=>246840
[1,3,7,4,2,6,5]=>258060
[1,3,7,4,5,2,6]=>290400
[1,3,7,4,5,6,2]=>343200
[1,3,7,4,6,2,5]=>318780
[1,3,7,4,6,5,2]=>360360
[1,3,7,5,2,4,6]=>278784
[1,3,7,5,2,6,4]=>304128
[1,3,7,5,4,2,6]=>309760
[1,3,7,5,4,6,2]=>366080
[1,3,7,5,6,2,4]=>371712
[1,3,7,5,6,4,2]=>402688
[1,3,7,6,2,4,5]=>326876
[1,3,7,6,2,5,4]=>341088
[1,3,7,6,4,2,5]=>361284
[1,3,7,6,4,5,2]=>408408
[1,3,7,6,5,2,4]=>394944
[1,3,7,6,5,4,2]=>427856
[1,4,2,3,5,6,7]=>110250
[1,4,2,3,5,7,6]=>115500
[1,4,2,3,6,5,7]=>117600
[1,4,2,3,6,7,5]=>128800
[1,4,2,3,7,5,6]=>130900
[1,4,2,3,7,6,5]=>136850
[1,4,2,5,3,6,7]=>132300
[1,4,2,5,3,7,6]=>138600
[1,4,2,5,6,3,7]=>158760
[1,4,2,5,6,7,3]=>189000
[1,4,2,5,7,3,6]=>175560
[1,4,2,5,7,6,3]=>199500
[1,4,2,6,3,5,7]=>152880
[1,4,2,6,3,7,5]=>167440
[1,4,2,6,5,3,7]=>171990
[1,4,2,6,5,7,3]=>204750
[1,4,2,6,7,3,5]=>209300
[1,4,2,6,7,5,3]=>227500
[1,4,2,7,3,5,6]=>183260
[1,4,2,7,3,6,5]=>191590
[1,4,2,7,5,3,6]=>204820
[1,4,2,7,5,6,3]=>232750
[1,4,2,7,6,3,5]=>225400
[1,4,2,7,6,5,3]=>245000
[1,4,3,2,5,6,7]=>126000
[1,4,3,2,5,7,6]=>132000
[1,4,3,2,6,5,7]=>134400
[1,4,3,2,6,7,5]=>147200
[1,4,3,2,7,5,6]=>149600
[1,4,3,2,7,6,5]=>156400
[1,4,3,5,2,6,7]=>163800
[1,4,3,5,2,7,6]=>171600
[1,4,3,5,6,2,7]=>207480
[1,4,3,5,6,7,2]=>256880
[1,4,3,5,7,2,6]=>228800
[1,4,3,5,7,6,2]=>270400
[1,4,3,6,2,5,7]=>188160
[1,4,3,6,2,7,5]=>206080
[1,4,3,6,5,2,7]=>223440
[1,4,3,6,5,7,2]=>276640
[1,4,3,6,7,2,5]=>270480
[1,4,3,6,7,5,2]=>305760
[1,4,3,7,2,5,6]=>224400
[1,4,3,7,2,6,5]=>234600
[1,4,3,7,5,2,6]=>264000
[1,4,3,7,5,6,2]=>312000
[1,4,3,7,6,2,5]=>289800
[1,4,3,7,6,5,2]=>327600
[1,4,5,2,3,6,7]=>189000
[1,4,5,2,3,7,6]=>198000
[1,4,5,2,6,3,7]=>226800
[1,4,5,2,6,7,3]=>270000
[1,4,5,2,7,3,6]=>250800
[1,4,5,2,7,6,3]=>285000
[1,4,5,3,2,6,7]=>204750
[1,4,5,3,2,7,6]=>214500
[1,4,5,3,6,2,7]=>259350
[1,4,5,3,6,7,2]=>321100
[1,4,5,3,7,2,6]=>286000
[1,4,5,3,7,6,2]=>338000
[1,4,5,6,2,3,7]=>302400
[1,4,5,6,2,7,3]=>360000
[1,4,5,6,3,2,7]=>319200
[1,4,5,6,3,7,2]=>395200
[1,4,5,6,7,2,3]=>460000
[1,4,5,6,7,3,2]=>478400
[1,4,5,7,2,3,6]=>355300
[1,4,5,7,2,6,3]=>403750
[1,4,5,7,3,2,6]=>374000
[1,4,5,7,3,6,2]=>442000
[1,4,5,7,6,2,3]=>488750
[1,4,5,7,6,3,2]=>508300
[1,4,6,2,3,5,7]=>240240
[1,4,6,2,3,7,5]=>263120
[1,4,6,2,5,3,7]=>270270
[1,4,6,2,5,7,3]=>321750
[1,4,6,2,7,3,5]=>328900
[1,4,6,2,7,5,3]=>357500
[1,4,6,3,2,5,7]=>258720
[1,4,6,3,2,7,5]=>283360
[1,4,6,3,5,2,7]=>307230
[1,4,6,3,5,7,2]=>380380
[1,4,6,3,7,2,5]=>371910
[1,4,6,3,7,5,2]=>420420
[1,4,6,5,2,3,7]=>332640
[1,4,6,5,2,7,3]=>396000
[1,4,6,5,3,2,7]=>351120
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Description
The product of the prefix sums of a permutation.
This is, given a permutation $\pi$ of length $n$,
$$ \prod_{i=1}^{n-1}(\pi(1)+\dots+\pi(i)).$$
This is, given a permutation $\pi$ of length $n$,
$$ \prod_{i=1}^{n-1}(\pi(1)+\dots+\pi(i)).$$
References
[1] Halder, A. Sum over permutations involving sign MathOverflow:344474
Code
def statistic(pi):
pi = list(pi)
return prod(sum(pi[:i]) for i in range(1,len(pi)))
Created
Oct 24, 2019 at 09:18 by Christian Stump
Updated
Oct 24, 2019 at 09:18 by Christian Stump
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