- FindStat

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Identifier

St001808: Dyck paths ⟶ ℤ

Values

=>
                            Cc0005;cc-rep
                            
                            
                            

                        [1,0,1,0]=>2
[1,1,0,0]=>1
[1,0,1,0,1,0]=>6
[1,0,1,1,0,0]=>4
[1,1,0,0,1,0]=>3
[1,1,0,1,0,0]=>2
[1,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,0]=>24
[1,0,1,0,1,1,0,0]=>18
[1,0,1,1,0,0,1,0]=>16
[1,0,1,1,0,1,0,0]=>12
[1,0,1,1,1,0,0,0]=>8
[1,1,0,0,1,0,1,0]=>12
[1,1,0,0,1,1,0,0]=>9
[1,1,0,1,0,0,1,0]=>8
[1,1,0,1,0,1,0,0]=>6
[1,1,0,1,1,0,0,0]=>4
[1,1,1,0,0,0,1,0]=>4
[1,1,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,0]=>120
[1,0,1,0,1,0,1,1,0,0]=>96
[1,0,1,0,1,1,0,0,1,0]=>90
[1,0,1,0,1,1,0,1,0,0]=>72
[1,0,1,0,1,1,1,0,0,0]=>54
[1,0,1,1,0,0,1,0,1,0]=>80
[1,0,1,1,0,0,1,1,0,0]=>64
[1,0,1,1,0,1,0,0,1,0]=>60
[1,0,1,1,0,1,0,1,0,0]=>48
[1,0,1,1,0,1,1,0,0,0]=>36
[1,0,1,1,1,0,0,0,1,0]=>40
[1,0,1,1,1,0,0,1,0,0]=>32
[1,0,1,1,1,0,1,0,0,0]=>24
[1,0,1,1,1,1,0,0,0,0]=>16
[1,1,0,0,1,0,1,0,1,0]=>60
[1,1,0,0,1,0,1,1,0,0]=>48
[1,1,0,0,1,1,0,0,1,0]=>45
[1,1,0,0,1,1,0,1,0,0]=>36
[1,1,0,0,1,1,1,0,0,0]=>27
[1,1,0,1,0,0,1,0,1,0]=>40
[1,1,0,1,0,0,1,1,0,0]=>32
[1,1,0,1,0,1,0,0,1,0]=>30
[1,1,0,1,0,1,0,1,0,0]=>24
[1,1,0,1,0,1,1,0,0,0]=>18
[1,1,0,1,1,0,0,0,1,0]=>20
[1,1,0,1,1,0,0,1,0,0]=>16
[1,1,0,1,1,0,1,0,0,0]=>12
[1,1,0,1,1,1,0,0,0,0]=>8
[1,1,1,0,0,0,1,0,1,0]=>20
[1,1,1,0,0,0,1,1,0,0]=>16
[1,1,1,0,0,1,0,0,1,0]=>15
[1,1,1,0,0,1,0,1,0,0]=>12
[1,1,1,0,0,1,1,0,0,0]=>9
[1,1,1,0,1,0,0,0,1,0]=>10
[1,1,1,0,1,0,0,1,0,0]=>8
[1,1,1,0,1,0,1,0,0,0]=>6
[1,1,1,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,0]=>5
[1,1,1,1,0,0,0,1,0,0]=>4
[1,1,1,1,0,0,1,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0]=>720
[1,0,1,0,1,0,1,0,1,1,0,0]=>600
[1,0,1,0,1,0,1,1,0,0,1,0]=>576
[1,0,1,0,1,0,1,1,0,1,0,0]=>480
[1,0,1,0,1,0,1,1,1,0,0,0]=>384
[1,0,1,0,1,1,0,0,1,0,1,0]=>540
[1,0,1,0,1,1,0,0,1,1,0,0]=>450
[1,0,1,0,1,1,0,1,0,0,1,0]=>432
[1,0,1,0,1,1,0,1,0,1,0,0]=>360
[1,0,1,0,1,1,0,1,1,0,0,0]=>288
[1,0,1,0,1,1,1,0,0,0,1,0]=>324
[1,0,1,0,1,1,1,0,0,1,0,0]=>270
[1,0,1,0,1,1,1,0,1,0,0,0]=>216
[1,0,1,0,1,1,1,1,0,0,0,0]=>162
[1,0,1,1,0,0,1,0,1,0,1,0]=>480
[1,0,1,1,0,0,1,0,1,1,0,0]=>400
[1,0,1,1,0,0,1,1,0,0,1,0]=>384
[1,0,1,1,0,0,1,1,0,1,0,0]=>320
[1,0,1,1,0,0,1,1,1,0,0,0]=>256
[1,0,1,1,0,1,0,0,1,0,1,0]=>360
[1,0,1,1,0,1,0,0,1,1,0,0]=>300
[1,0,1,1,0,1,0,1,0,0,1,0]=>288
[1,0,1,1,0,1,0,1,0,1,0,0]=>240
[1,0,1,1,0,1,0,1,1,0,0,0]=>192
[1,0,1,1,0,1,1,0,0,0,1,0]=>216
[1,0,1,1,0,1,1,0,0,1,0,0]=>180
[1,0,1,1,0,1,1,0,1,0,0,0]=>144
[1,0,1,1,0,1,1,1,0,0,0,0]=>108
[1,0,1,1,1,0,0,0,1,0,1,0]=>240
[1,0,1,1,1,0,0,0,1,1,0,0]=>200
[1,0,1,1,1,0,0,1,0,0,1,0]=>192
[1,0,1,1,1,0,0,1,0,1,0,0]=>160
[1,0,1,1,1,0,0,1,1,0,0,0]=>128
[1,0,1,1,1,0,1,0,0,0,1,0]=>144
[1,0,1,1,1,0,1,0,0,1,0,0]=>120
[1,0,1,1,1,0,1,0,1,0,0,0]=>96
[1,0,1,1,1,0,1,1,0,0,0,0]=>72
[1,0,1,1,1,1,0,0,0,0,1,0]=>96
[1,0,1,1,1,1,0,0,0,1,0,0]=>80
[1,0,1,1,1,1,0,0,1,0,0,0]=>64
[1,0,1,1,1,1,0,1,0,0,0,0]=>48
[1,0,1,1,1,1,1,0,0,0,0,0]=>32
[1,1,0,0,1,0,1,0,1,0,1,0]=>360
[1,1,0,0,1,0,1,0,1,1,0,0]=>300
[1,1,0,0,1,0,1,1,0,0,1,0]=>288
[1,1,0,0,1,0,1,1,0,1,0,0]=>240
[1,1,0,0,1,0,1,1,1,0,0,0]=>192
[1,1,0,0,1,1,0,0,1,0,1,0]=>270
[1,1,0,0,1,1,0,0,1,1,0,0]=>225
[1,1,0,0,1,1,0,1,0,0,1,0]=>216
[1,1,0,0,1,1,0,1,0,1,0,0]=>180
[1,1,0,0,1,1,0,1,1,0,0,0]=>144
[1,1,0,0,1,1,1,0,0,0,1,0]=>162
[1,1,0,0,1,1,1,0,0,1,0,0]=>135
[1,1,0,0,1,1,1,0,1,0,0,0]=>108
[1,1,0,0,1,1,1,1,0,0,0,0]=>81
[1,1,0,1,0,0,1,0,1,0,1,0]=>240
[1,1,0,1,0,0,1,0,1,1,0,0]=>200
[1,1,0,1,0,0,1,1,0,0,1,0]=>192
[1,1,0,1,0,0,1,1,0,1,0,0]=>160
[1,1,0,1,0,0,1,1,1,0,0,0]=>128
[1,1,0,1,0,1,0,0,1,0,1,0]=>180
[1,1,0,1,0,1,0,0,1,1,0,0]=>150
[1,1,0,1,0,1,0,1,0,0,1,0]=>144
[1,1,0,1,0,1,0,1,0,1,0,0]=>120
[1,1,0,1,0,1,0,1,1,0,0,0]=>96
[1,1,0,1,0,1,1,0,0,0,1,0]=>108
[1,1,0,1,0,1,1,0,0,1,0,0]=>90
[1,1,0,1,0,1,1,0,1,0,0,0]=>72
[1,1,0,1,0,1,1,1,0,0,0,0]=>54
[1,1,0,1,1,0,0,0,1,0,1,0]=>120
[1,1,0,1,1,0,0,0,1,1,0,0]=>100
[1,1,0,1,1,0,0,1,0,0,1,0]=>96
[1,1,0,1,1,0,0,1,0,1,0,0]=>80
[1,1,0,1,1,0,0,1,1,0,0,0]=>64
[1,1,0,1,1,0,1,0,0,0,1,0]=>72
[1,1,0,1,1,0,1,0,0,1,0,0]=>60
[1,1,0,1,1,0,1,0,1,0,0,0]=>48
[1,1,0,1,1,0,1,1,0,0,0,0]=>36
[1,1,0,1,1,1,0,0,0,0,1,0]=>48
[1,1,0,1,1,1,0,0,0,1,0,0]=>40
[1,1,0,1,1,1,0,0,1,0,0,0]=>32
[1,1,0,1,1,1,0,1,0,0,0,0]=>24
[1,1,0,1,1,1,1,0,0,0,0,0]=>16
[1,1,1,0,0,0,1,0,1,0,1,0]=>120
[1,1,1,0,0,0,1,0,1,1,0,0]=>100
[1,1,1,0,0,0,1,1,0,0,1,0]=>96
[1,1,1,0,0,0,1,1,0,1,0,0]=>80
[1,1,1,0,0,0,1,1,1,0,0,0]=>64
[1,1,1,0,0,1,0,0,1,0,1,0]=>90
[1,1,1,0,0,1,0,0,1,1,0,0]=>75
[1,1,1,0,0,1,0,1,0,0,1,0]=>72
[1,1,1,0,0,1,0,1,0,1,0,0]=>60
[1,1,1,0,0,1,0,1,1,0,0,0]=>48
[1,1,1,0,0,1,1,0,0,0,1,0]=>54
[1,1,1,0,0,1,1,0,0,1,0,0]=>45
[1,1,1,0,0,1,1,0,1,0,0,0]=>36
[1,1,1,0,0,1,1,1,0,0,0,0]=>27
[1,1,1,0,1,0,0,0,1,0,1,0]=>60
[1,1,1,0,1,0,0,0,1,1,0,0]=>50
[1,1,1,0,1,0,0,1,0,0,1,0]=>48
[1,1,1,0,1,0,0,1,0,1,0,0]=>40
[1,1,1,0,1,0,0,1,1,0,0,0]=>32
[1,1,1,0,1,0,1,0,0,0,1,0]=>36
[1,1,1,0,1,0,1,0,0,1,0,0]=>30
[1,1,1,0,1,0,1,0,1,0,0,0]=>24
[1,1,1,0,1,0,1,1,0,0,0,0]=>18
[1,1,1,0,1,1,0,0,0,0,1,0]=>24
[1,1,1,0,1,1,0,0,0,1,0,0]=>20
[1,1,1,0,1,1,0,0,1,0,0,0]=>16
[1,1,1,0,1,1,0,1,0,0,0,0]=>12
[1,1,1,0,1,1,1,0,0,0,0,0]=>8
[1,1,1,1,0,0,0,0,1,0,1,0]=>30
[1,1,1,1,0,0,0,0,1,1,0,0]=>25
[1,1,1,1,0,0,0,1,0,0,1,0]=>24
[1,1,1,1,0,0,0,1,0,1,0,0]=>20
[1,1,1,1,0,0,0,1,1,0,0,0]=>16
[1,1,1,1,0,0,1,0,0,0,1,0]=>18
[1,1,1,1,0,0,1,0,0,1,0,0]=>15
[1,1,1,1,0,0,1,0,1,0,0,0]=>12
[1,1,1,1,0,0,1,1,0,0,0,0]=>9
[1,1,1,1,0,1,0,0,0,0,1,0]=>12
[1,1,1,1,0,1,0,0,0,1,0,0]=>10
[1,1,1,1,0,1,0,0,1,0,0,0]=>8
[1,1,1,1,0,1,0,1,0,0,0,0]=>6
[1,1,1,1,0,1,1,0,0,0,0,0]=>4
[1,1,1,1,1,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,1,1,1,1,0,0,0,1,0,0,0]=>4
[1,1,1,1,1,0,0,1,0,0,0,0]=>3
[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>5040
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>4320
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>4200
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>3600
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>3000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>4032
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>3456
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>3360
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>2880
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2400
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2688
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2304
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>1920
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>1536
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>3780
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>3240
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>3150
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2700
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>2250
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>3024
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2592
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>2520
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>2160
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>1800
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2016
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>1728
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>1440
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>1152
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2268
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>1944
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>1890
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>1620
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>1350
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>1512
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>1296
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>1080
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>864
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>1134
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>972
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>810
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>648
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>486
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>3360
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2880
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2800
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2400
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>2000
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2688
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>2304
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2240
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>1920
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>1600
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>1792
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>1536
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>1280
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>1024
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2520
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2160
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2100
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>1800
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>1500
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>2016
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>1728
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1680
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1440
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>1200
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>1344
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>1152
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>960
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>768
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>1512
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>1296
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>1260
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>1080
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>900
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>1008
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>864
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>720
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>576
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>756
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>648
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>540
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>432
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>324
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>1680
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>1440
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>1400
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>1200
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>1000
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>1344
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>1152
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>1120
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>960
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>800
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>896
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>768
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>640
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>512
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>1008
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>864
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>840
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>720
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>600
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>672
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>576
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>480
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>384
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>504
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>432
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>360
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>288
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>216
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>672
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>576
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>560
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>480
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>400
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>448
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>384
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>320
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>256
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>336
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>288
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>240
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>192
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>144
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>224
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>192
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>160
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>128
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>96
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>64
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2520
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2160
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2100
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>1800
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>1500
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2016
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>1728
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>1680
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>1440
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>1200
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>1344
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>1152
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>960
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>768
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>1890
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>1620
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>1575
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>1350
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>1125
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>1512
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>1296
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>1260
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>1080
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>900
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>1008
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>864
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>720
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>576
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>1134
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>972
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>945
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>810
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>675
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>756
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>648
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>540
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>432
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>567
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>486
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>405
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>324
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>243
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1680
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>1440
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>1400
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>1200
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>1000
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1344
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>1152
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>1120
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>960
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>800
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>896
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>768
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>640
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>512
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1260
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>1080
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>1050
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>900
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>750
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1008
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>864
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>840
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>720
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>600
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>672
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>576
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>480
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>384
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>756
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>648
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>630
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>540
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>450
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>504
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>432
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>360
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>288
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>378
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>324
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>270
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>216
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>162
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>840
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>720
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>700
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>600
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>500
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>672
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>576
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>560
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>480
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>400
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>448
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>384
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>320
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>256
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>504
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>432
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>420
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>360
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>300
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>336
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>288
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>240
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>192
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>252
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>216
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>180
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>144
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>108
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>336
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>288
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>280
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>240
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>200
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>224
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>192
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>160
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>128
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>168
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>144
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>120
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>96
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>72
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>112
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>96
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>80
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>64
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>48
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>32
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>840
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>720
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>700
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>600
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>500
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>672
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>576
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>560
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>480
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>400
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>448
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>384
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>320
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>256
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>630
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>540
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>525
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>450
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>375
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>504
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>432
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>420
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>360
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>300
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>336
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>288
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>240
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>192
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>378
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>324
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>315
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>270
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>225
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>252
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>216
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>180
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>144
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>189
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>162
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>135
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>108
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>81
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>420
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>360
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>350
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>300
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>250
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>336
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>288
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>280
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>240
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>200
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>224
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>192
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>160
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>128
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>252
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>216
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>210
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>180
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>150
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>168
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>144
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>120
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>96
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>126
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>108
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>90
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>72
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>54
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>168
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>144
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>140
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>120
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>100
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>112
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>96
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>80
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>64
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>84
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>72
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>60
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>48
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>36
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>56
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>48
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>40
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>32
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>24
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>16
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>210
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>180
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>175
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>150
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>125
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>168
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>144
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>140
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>120
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>100
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>112
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>96
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>80
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>64
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>126
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>108
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>105
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>90
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>75
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>84
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>72
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>60
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>48
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>63
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>54
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>45
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>36
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>27
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>84
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>72
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>70
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>60
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>50
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>56
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>48
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>40
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>32
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>42
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>36
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>30
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>24
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>18
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>28
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>24
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>20
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>16
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>12
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>42
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>36
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>35
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>30
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>25
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>28
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>24
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>20
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>16
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>21
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>18
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>15
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>12
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>9
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>14
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>12
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>10
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>8
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>7
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>40320
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>35280
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>34560
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>30240
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>25920
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>33600
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>29400
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>28800
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>25200
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>21600
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>24000
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>21000
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>18000
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>15000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>32256
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>28224
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>27648
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>24192
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>20736
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>26880
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>23520
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>23040
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>20160
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>17280
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>19200
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>16800
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>14400
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>12000
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>21504
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>18816
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>18432
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>16128
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>13824
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>15360
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>13440
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>11520
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>9600
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>12288
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>10752
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>9216
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>7680
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>6144
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>30240
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>26460
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>25920
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>22680
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>19440
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>25200
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>22050
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>21600
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>18900
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>16200
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>18000
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>15750
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>13500
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>11250
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>24192
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>21168
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>20736
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>18144
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>15552
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>20160
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>17640
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>17280
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>15120
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>12960
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>14400
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>12600
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>10800
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>9000
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>16128
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>14112
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>13824
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>12096
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>10368
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>11520
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>10080
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>8640
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>7200
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>9216
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>8064
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>6912
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>5760
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>4608
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>18144
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>15876
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>15552
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>13608
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>11664
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>15120
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>13230
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>12960
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>11340
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>9720
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>10800
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>9450
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>8100
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>6750
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>12096
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>10584
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>10368
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>9072
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>7776
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>8640
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>7560
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>6480
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>5400
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>6912
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>6048
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>5184
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>4320
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>3456
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>9072
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>7938
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>7776
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>6804
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>5832
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>6480
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>5670
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>4860
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>4050
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>5184
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>4536
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>3888
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3240
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>2592
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>3888
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>3402
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>2916
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>2430
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>1944
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1458
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>26880
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>23520
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>23040
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>20160
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>17280
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>22400
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>19600
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>19200
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>16800
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>14400
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>16000
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>14000
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>12000
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>10000
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>21504
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>18816
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>18432
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>16128
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>13824
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>17920
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>15680
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>15360
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>13440
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>11520
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>12800
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>11200
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>9600
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>8000
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>14336
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>12544
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>12288
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>10752
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>9216
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>10240
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>8960
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>7680
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>6400
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>8192
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>7168
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>6144
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>5120
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>4096
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>20160
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>17640
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>17280
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>15120
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>12960
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>16800
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>14700
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>14400
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>12600
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>10800
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>12000
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>10500
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>9000
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>7500
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>16128
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>14112
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>13824
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>12096
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>10368
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>13440
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>11760
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>11520
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>10080
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>8640
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>9600
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>8400
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>7200
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>6000
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>10752
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>9408
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>9216
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>8064
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>6912
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>7680
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>6720
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>5760
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>4800
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>6144
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>5376
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>4608
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>3840
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>3072
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>12096
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>10584
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>10368
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>9072
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>7776
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>10080
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>8820
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>8640
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>7560
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>6480
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>7200
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>6300
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>5400
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>4500
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>8064
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>7056
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>6912
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>6048
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>5184
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>5760
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>5040
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>4320
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>3600
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>4608
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>4032
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>3456
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>2880
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>2304
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>6048
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>5292
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>5184
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>4536
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>3888
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>4320
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>3780
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>3240
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>2700
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>3456
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>3024
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>2592
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>2160
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>1728
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>2592
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>2268
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>1944
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>1620
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>1296
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>972
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>13440
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>11760
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>11520
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>10080
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>8640
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>11200
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>9800
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>9600
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>8400
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>7200
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>8000
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>7000
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>6000
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>5000
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>10752
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>9408
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>9216
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>8064
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>6912
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>8960
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>7840
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>7680
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>6720
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>5760
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>6400
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>5600
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>4800
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>4000
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>7168
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>6272
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>6144
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>5376
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>4608
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>5120
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>4480
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>3840
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>3200
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>4096
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>3584
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>3072
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>2560
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>2048
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>8064
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>7056
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>6912
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>6048
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>5184
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>6720
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>5880
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>5760
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>5040
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>4320
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>4800
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>4200
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3600
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>3000
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>5376
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>4704
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>4608
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>4032
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>3456
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>3840
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>3360
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2880
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>2400
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>3072
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>2688
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>2304
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>1920
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>1536
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>4032
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>3528
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>3456
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>3024
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>2592
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>2880
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>2520
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>2160
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>1800
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>2304
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>2016
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>1728
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>1440
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>1152
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>1728
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>1512
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>1296
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>1080
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>864
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>648
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>5376
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>4704
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>4608
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>4032
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>3456
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>4480
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>3920
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>3840
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>3360
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>2880
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>3200
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>2800
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>2400
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>2000
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>3584
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>3136
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>3072
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>2688
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>2304
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>2560
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>2240
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>1920
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>1600
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>2048
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>1792
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>1536
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>1280
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>1024
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>2688
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>2352
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>2304
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>2016
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>1728
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>1920
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>1680
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>1440
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>1200
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>1536
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>1344
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>1152
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>960
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>768
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>1152
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>1008
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>864
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>720
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>576
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>432
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>1792
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>1568
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>1536
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>1344
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>1152
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>1280
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>1120
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>960
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>800
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>1024
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>896
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>768
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>640
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>512
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>768
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>672
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>576
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>480
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>384
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>288
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>512
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>448
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>384
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>320
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>256
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>192
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>128
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>20160
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>17640
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>17280
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>15120
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>12960
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>16800
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>14700
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>14400
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>12600
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>10800
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>12000
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>10500
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>9000
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>7500
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>16128
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>14112
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>13824
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>12096
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>10368
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>13440
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>11760
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>11520
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>10080
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>8640
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>9600
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>8400
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>7200
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>6000
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>10752
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>9408
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>9216
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>8064
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>6912
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>7680
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>6720
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>5760
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>4800
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>6144
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>5376
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>4608
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>3840
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>3072
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>15120
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>13230
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>12960
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>11340
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>9720
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>12600
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>11025
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>10800
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>9450
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>8100
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>9000
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>7875
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>6750
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>5625
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>12096
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>10584
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>10368
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>9072
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>7776
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>10080
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>8820
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>8640
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>7560
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>6480
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>7200
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>6300
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>5400
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>4500
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>8064
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>7056
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>6912
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>6048
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>5184
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>5760
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>5040
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>4320
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3600
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>4608
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>4032
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>3456
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>2880
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>2304
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>9072
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>7938
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>7776
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>6804
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>5832
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>7560
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>6615
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>6480
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>5670
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>4860
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>5400
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>4725
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>4050
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>3375
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>6048
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>5292
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>5184
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>4536
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>3888
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>4320
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>3780
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>3240
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>2700
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>3456
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3024
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>2592
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>2160
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>1728
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>4536
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>3969
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>3888
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>3402
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>2916
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>3240
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>2835
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>2430
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>2025
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>2592
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>2268
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>1944
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>1620
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>1296
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>1944
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>1701
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>1458
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>1215
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>972
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>729
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>13440
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>11760
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>11520
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>10080
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>8640
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>11200
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>9800
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>9600
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>8400
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>7200
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>8000
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>7000
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>6000
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>5000
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>10752
                    

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$F_{2} = q + q^{2}$

$F_{3} = q + q^{2} + q^{3} + q^{4} + q^{6}$

$F_{4} = q + q^{2} + q^{3} + 2\ q^{4} + q^{6} + 2\ q^{8} + q^{9} + 2\ q^{12} + q^{16} + q^{18} + q^{24}$

$F_{5} = q + q^{2} + q^{3} + 2\ q^{4} + q^{5} + q^{6} + 2\ q^{8} + q^{9} + q^{10} + 2\ q^{12} + q^{15} + 3\ q^{16} + q^{18} + 2\ q^{20} + 2\ q^{24} + q^{27} + q^{30} + 2\ q^{32} + 2\ q^{36} + 2\ q^{40} + q^{45} + 2\ q^{48} + q^{54} + 2\ q^{60} + q^{64} + q^{72} + q^{80} + q^{90} + q^{96} + q^{120}$

$F_{6} = q + q^{2} + q^{3} + 2\ q^{4} + q^{5} + 2\ q^{6} + 2\ q^{8} + q^{9} + q^{10} + 3\ q^{12} + q^{15} + 3\ q^{16} + 2\ q^{18} + 2\ q^{20} + 4\ q^{24} + q^{25} + q^{27} + 2\ q^{30} + 3\ q^{32} + 3\ q^{36} + 2\ q^{40} + q^{45} + 5\ q^{48} + q^{50} + 2\ q^{54} + 3\ q^{60} + 3\ q^{64} + 4\ q^{72} + q^{75} + 3\ q^{80} + q^{81} + 2\ q^{90} + 5\ q^{96} + 2\ q^{100} + 3\ q^{108} + 4\ q^{120} + 2\ q^{128} + q^{135} + 4\ q^{144} + q^{150} + 2\ q^{160} + 2\ q^{162} + 3\ q^{180} + 4\ q^{192} + 2\ q^{200} + 3\ q^{216} + q^{225} + 4\ q^{240} + q^{256} + 2\ q^{270} + 3\ q^{288} + 2\ q^{300} + q^{320} + q^{324} + 3\ q^{360} + 2\ q^{384} + q^{400} + q^{432} + q^{450} + 2\ q^{480} + q^{540} + q^{576} + q^{600} + q^{720}$

$F_{7} = q + q^{2} + q^{3} + 2\ q^{4} + q^{5} + 2\ q^{6} + q^{7} + 2\ q^{8} + q^{9} + q^{10} + 3\ q^{12} + q^{14} + q^{15} + 3\ q^{16} + 2\ q^{18} + 2\ q^{20} + q^{21} + 4\ q^{24} + q^{25} + q^{27} + 2\ q^{28} + 2\ q^{30} + 3\ q^{32} + q^{35} + 4\ q^{36} + 2\ q^{40} + 2\ q^{42} + q^{45} + 5\ q^{48} + q^{50} + 2\ q^{54} + 2\ q^{56} + 3\ q^{60} + q^{63} + 4\ q^{64} + q^{70} + 5\ q^{72} + q^{75} + 3\ q^{80} + q^{81} + 3\ q^{84} + 2\ q^{90} + 6\ q^{96} + 2\ q^{100} + q^{105} + 4\ q^{108} + 3\ q^{112} + 4\ q^{120} + q^{125} + 2\ q^{126} + 3\ q^{128} + q^{135} + 2\ q^{140} + 7\ q^{144} + 2\ q^{150} + 3\ q^{160} + 2\ q^{162} + 4\ q^{168} + q^{175} + 4\ q^{180} + q^{189} + 6\ q^{192} + 2\ q^{200} + 2\ q^{210} + 5\ q^{216} + 3\ q^{224} + q^{225} + 5\ q^{240} + q^{243} + q^{250} + 3\ q^{252} + 3\ q^{256} + 2\ q^{270} + 2\ q^{280} + 7\ q^{288} + 3\ q^{300} + q^{315} + 3\ q^{320} + 4\ q^{324} + 5\ q^{336} + q^{350} + 5\ q^{360} + q^{375} + 2\ q^{378} + 5\ q^{384} + 3\ q^{400} + q^{405} + 3\ q^{420} + 6\ q^{432} + 3\ q^{448} + 2\ q^{450} + 5\ q^{480} + 2\ q^{486} + 2\ q^{500} + 4\ q^{504} + 2\ q^{512} + q^{525} + 4\ q^{540} + 3\ q^{560} + q^{567} + 7\ q^{576} + 4\ q^{600} + 2\ q^{630} + 2\ q^{640} + 4\ q^{648} + 5\ q^{672} + q^{675} + 2\ q^{700} + 6\ q^{720} + q^{750} + 3\ q^{756} + 4\ q^{768} + 2\ q^{800} + 2\ q^{810} + 4\ q^{840} + 5\ q^{864} + 2\ q^{896} + 3\ q^{900} + q^{945} + 4\ q^{960} + 2\ q^{972} + 2\ q^{1000} + 4\ q^{1008} + q^{1024} + q^{1050} + 4\ q^{1080} + 2\ q^{1120} + q^{1125} + 2\ q^{1134} + 5\ q^{1152} + 4\ q^{1200} + 3\ q^{1260} + q^{1280} + 3\ q^{1296} + 4\ q^{1344} + 2\ q^{1350} + 2\ q^{1400} + 5\ q^{1440} + 2\ q^{1500} + 3\ q^{1512} + 2\ q^{1536} + q^{1575} + q^{1600} + 2\ q^{1620} + 4\ q^{1680} + 3\ q^{1728} + q^{1792} + 3\ q^{1800} + 2\ q^{1890} + 2\ q^{1920} + q^{1944} + q^{2000} + 3\ q^{2016} + 2\ q^{2100} + 3\ q^{2160} + q^{2240} + q^{2250} + q^{2268} + 2\ q^{2304} + 2\ q^{2400} + 3\ q^{2520} + q^{2592} + 2\ q^{2688} + q^{2700} + q^{2800} + 2\ q^{2880} + q^{3000} + q^{3024} + q^{3150} + q^{3240} + 2\ q^{3360} + q^{3456} + q^{3600} + q^{3780} + q^{4032} + q^{4200} + q^{4320} + q^{5040}$

Description

The box weight or horizontal decoration of a Dyck path.
Let a Dyck path $D = (d_1,d_2,\dots,d_n)$ with steps $d_i \in \{N=(0,1),E=(1,0)\}$ be given.
For the $i$th step $d_i \in D$ we define the weight
$$ \beta(d_i) = 1, \quad \text{ if } d_i=N, $$
and
$$ \beta(d_i) = \sum_{k = 1}^{i} [\![ d_k = N]\!], \quad \text{ if } d_i=E, $$
where we use the Iverson bracket $[\![ A ]\!]$ that is equal to $1$ if $A$ is true, and $0$ otherwise.
The box weight or horizontal deocration of $D$ is defined as
$$ \prod_{i=1}^{n} \beta(d_i). $$
The name describes the fact that between each $E$ step and the line $y=-1$ exactly one unit box is marked.

References

[1] Elvey Price, A., Fang, W., Wallner, M. Compacted binary trees admit a stretched exponential arXiv:1908.11181
[2] doi:10.4230/LIPIcs.AofA.2020.11
[3] Number of deterministic completely defined initially connected acyclic automata with 2 inputs and n transient unlabeled states (and a unique absorbing state). OEIS:A082161

Code

def dyck_box_weight(x):
    xw = 1
    lvl = 1
    for step in x:
        if step == 0:
            lvl += 1
        else:
            xw *= lvl
    return xw

Created

Jun 13, 2022 at 14:21 by Michael Wallner

Updated

Jun 13, 2022 at 14:21 by Michael Wallner