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Identifier

St000419: Dyck paths ⟶ ℤ (values match St000420The number of Dyck paths that are weakly above a Dyck path.)

Values

=>
                            Cc0005;cc-rep
                            
                            
                            

                        [1,0,1,0]=>1
[1,1,0,0]=>0
[1,0,1,0,1,0]=>4
[1,0,1,1,0,0]=>2
[1,1,0,0,1,0]=>2
[1,1,0,1,0,0]=>1
[1,1,1,0,0,0]=>0
[1,0,1,0,1,0,1,0]=>13
[1,0,1,0,1,1,0,0]=>8
[1,0,1,1,0,0,1,0]=>9
[1,0,1,1,0,1,0,0]=>6
[1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,0]=>5
[1,1,0,1,0,0,1,0]=>6
[1,1,0,1,0,1,0,0]=>4
[1,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,0]=>3
[1,1,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0]=>41
[1,0,1,0,1,0,1,1,0,0]=>27
[1,0,1,0,1,1,0,0,1,0]=>31
[1,0,1,0,1,1,0,1,0,0]=>22
[1,0,1,0,1,1,1,0,0,0]=>13
[1,0,1,1,0,0,1,0,1,0]=>31
[1,0,1,1,0,0,1,1,0,0]=>21
[1,0,1,1,0,1,0,0,1,0]=>25
[1,0,1,1,0,1,0,1,0,0]=>18
[1,0,1,1,0,1,1,0,0,0]=>11
[1,0,1,1,1,0,0,0,1,0]=>16
[1,0,1,1,1,0,0,1,0,0]=>12
[1,0,1,1,1,0,1,0,0,0]=>8
[1,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,0,1,0,1,0]=>27
[1,1,0,0,1,0,1,1,0,0]=>18
[1,1,0,0,1,1,0,0,1,0]=>21
[1,1,0,0,1,1,0,1,0,0]=>15
[1,1,0,0,1,1,1,0,0,0]=>9
[1,1,0,1,0,0,1,0,1,0]=>22
[1,1,0,1,0,0,1,1,0,0]=>15
[1,1,0,1,0,1,0,0,1,0]=>18
[1,1,0,1,0,1,0,1,0,0]=>13
[1,1,0,1,0,1,1,0,0,0]=>8
[1,1,0,1,1,0,0,0,1,0]=>12
[1,1,0,1,1,0,0,1,0,0]=>9
[1,1,0,1,1,0,1,0,0,0]=>6
[1,1,0,1,1,1,0,0,0,0]=>3
[1,1,1,0,0,0,1,0,1,0]=>13
[1,1,1,0,0,0,1,1,0,0]=>9
[1,1,1,0,0,1,0,0,1,0]=>11
[1,1,1,0,0,1,0,1,0,0]=>8
[1,1,1,0,0,1,1,0,0,0]=>5
[1,1,1,0,1,0,0,0,1,0]=>8
[1,1,1,0,1,0,0,1,0,0]=>6
[1,1,1,0,1,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,0]=>3
[1,1,1,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>131
[1,0,1,0,1,0,1,0,1,1,0,0]=>89
[1,0,1,0,1,0,1,1,0,0,1,0]=>103
[1,0,1,0,1,0,1,1,0,1,0,0]=>75
[1,0,1,0,1,0,1,1,1,0,0,0]=>47
[1,0,1,0,1,1,0,0,1,0,1,0]=>106
[1,0,1,0,1,1,0,0,1,1,0,0]=>74
[1,0,1,0,1,1,0,1,0,0,1,0]=>88
[1,0,1,0,1,1,0,1,0,1,0,0]=>65
[1,0,1,0,1,1,0,1,1,0,0,0]=>42
[1,0,1,0,1,1,1,0,0,0,1,0]=>61
[1,0,1,0,1,1,1,0,0,1,0,0]=>47
[1,0,1,0,1,1,1,0,1,0,0,0]=>33
[1,0,1,0,1,1,1,1,0,0,0,0]=>19
[1,0,1,1,0,0,1,0,1,0,1,0]=>103
[1,0,1,1,0,0,1,0,1,1,0,0]=>71
[1,0,1,1,0,0,1,1,0,0,1,0]=>83
[1,0,1,1,0,0,1,1,0,1,0,0]=>61
[1,0,1,1,0,0,1,1,1,0,0,0]=>39
[1,0,1,1,0,1,0,0,1,0,1,0]=>88
[1,0,1,1,0,1,0,0,1,1,0,0]=>62
[1,0,1,1,0,1,0,1,0,0,1,0]=>74
[1,0,1,1,0,1,0,1,0,1,0,0]=>55
[1,0,1,1,0,1,0,1,1,0,0,0]=>36
[1,0,1,1,0,1,1,0,0,0,1,0]=>53
[1,0,1,1,0,1,1,0,0,1,0,0]=>41
[1,0,1,1,0,1,1,0,1,0,0,0]=>29
[1,0,1,1,0,1,1,1,0,0,0,0]=>17
[1,0,1,1,1,0,0,0,1,0,1,0]=>61
[1,0,1,1,1,0,0,0,1,1,0,0]=>44
[1,0,1,1,1,0,0,1,0,0,1,0]=>53
[1,0,1,1,1,0,0,1,0,1,0,0]=>40
[1,0,1,1,1,0,0,1,1,0,0,0]=>27
[1,0,1,1,1,0,1,0,0,0,1,0]=>41
[1,0,1,1,1,0,1,0,0,1,0,0]=>32
[1,0,1,1,1,0,1,0,1,0,0,0]=>23
[1,0,1,1,1,0,1,1,0,0,0,0]=>14
[1,0,1,1,1,1,0,0,0,0,1,0]=>25
[1,0,1,1,1,1,0,0,0,1,0,0]=>20
[1,0,1,1,1,1,0,0,1,0,0,0]=>15
[1,0,1,1,1,1,0,1,0,0,0,0]=>10
[1,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,0,1,0,1,0,1,0,1,0]=>89
[1,1,0,0,1,0,1,0,1,1,0,0]=>61
[1,1,0,0,1,0,1,1,0,0,1,0]=>71
[1,1,0,0,1,0,1,1,0,1,0,0]=>52
[1,1,0,0,1,0,1,1,1,0,0,0]=>33
[1,1,0,0,1,1,0,0,1,0,1,0]=>74
[1,1,0,0,1,1,0,0,1,1,0,0]=>52
[1,1,0,0,1,1,0,1,0,0,1,0]=>62
[1,1,0,0,1,1,0,1,0,1,0,0]=>46
[1,1,0,0,1,1,0,1,1,0,0,0]=>30
[1,1,0,0,1,1,1,0,0,0,1,0]=>44
[1,1,0,0,1,1,1,0,0,1,0,0]=>34
[1,1,0,0,1,1,1,0,1,0,0,0]=>24
[1,1,0,0,1,1,1,1,0,0,0,0]=>14
[1,1,0,1,0,0,1,0,1,0,1,0]=>75
[1,1,0,1,0,0,1,0,1,1,0,0]=>52
[1,1,0,1,0,0,1,1,0,0,1,0]=>61
[1,1,0,1,0,0,1,1,0,1,0,0]=>45
[1,1,0,1,0,0,1,1,1,0,0,0]=>29
[1,1,0,1,0,1,0,0,1,0,1,0]=>65
[1,1,0,1,0,1,0,0,1,1,0,0]=>46
[1,1,0,1,0,1,0,1,0,0,1,0]=>55
[1,1,0,1,0,1,0,1,0,1,0,0]=>41
[1,1,0,1,0,1,0,1,1,0,0,0]=>27
[1,1,0,1,0,1,1,0,0,0,1,0]=>40
[1,1,0,1,0,1,1,0,0,1,0,0]=>31
[1,1,0,1,0,1,1,0,1,0,0,0]=>22
[1,1,0,1,0,1,1,1,0,0,0,0]=>13
[1,1,0,1,1,0,0,0,1,0,1,0]=>47
[1,1,0,1,1,0,0,0,1,1,0,0]=>34
[1,1,0,1,1,0,0,1,0,0,1,0]=>41
[1,1,0,1,1,0,0,1,0,1,0,0]=>31
[1,1,0,1,1,0,0,1,1,0,0,0]=>21
[1,1,0,1,1,0,1,0,0,0,1,0]=>32
[1,1,0,1,1,0,1,0,0,1,0,0]=>25
[1,1,0,1,1,0,1,0,1,0,0,0]=>18
[1,1,0,1,1,0,1,1,0,0,0,0]=>11
[1,1,0,1,1,1,0,0,0,0,1,0]=>20
[1,1,0,1,1,1,0,0,0,1,0,0]=>16
[1,1,0,1,1,1,0,0,1,0,0,0]=>12
[1,1,0,1,1,1,0,1,0,0,0,0]=>8
[1,1,0,1,1,1,1,0,0,0,0,0]=>4
[1,1,1,0,0,0,1,0,1,0,1,0]=>47
[1,1,1,0,0,0,1,0,1,1,0,0]=>33
[1,1,1,0,0,0,1,1,0,0,1,0]=>39
[1,1,1,0,0,0,1,1,0,1,0,0]=>29
[1,1,1,0,0,0,1,1,1,0,0,0]=>19
[1,1,1,0,0,1,0,0,1,0,1,0]=>42
[1,1,1,0,0,1,0,0,1,1,0,0]=>30
[1,1,1,0,0,1,0,1,0,0,1,0]=>36
[1,1,1,0,0,1,0,1,0,1,0,0]=>27
[1,1,1,0,0,1,0,1,1,0,0,0]=>18
[1,1,1,0,0,1,1,0,0,0,1,0]=>27
[1,1,1,0,0,1,1,0,0,1,0,0]=>21
[1,1,1,0,0,1,1,0,1,0,0,0]=>15
[1,1,1,0,0,1,1,1,0,0,0,0]=>9
[1,1,1,0,1,0,0,0,1,0,1,0]=>33
[1,1,1,0,1,0,0,0,1,1,0,0]=>24
[1,1,1,0,1,0,0,1,0,0,1,0]=>29
[1,1,1,0,1,0,0,1,0,1,0,0]=>22
[1,1,1,0,1,0,0,1,1,0,0,0]=>15
[1,1,1,0,1,0,1,0,0,0,1,0]=>23
[1,1,1,0,1,0,1,0,0,1,0,0]=>18
[1,1,1,0,1,0,1,0,1,0,0,0]=>13
[1,1,1,0,1,0,1,1,0,0,0,0]=>8
[1,1,1,0,1,1,0,0,0,0,1,0]=>15
[1,1,1,0,1,1,0,0,0,1,0,0]=>12
[1,1,1,0,1,1,0,0,1,0,0,0]=>9
[1,1,1,0,1,1,0,1,0,0,0,0]=>6
[1,1,1,0,1,1,1,0,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0,1,0]=>19
[1,1,1,1,0,0,0,0,1,1,0,0]=>14
[1,1,1,1,0,0,0,1,0,0,1,0]=>17
[1,1,1,1,0,0,0,1,0,1,0,0]=>13
[1,1,1,1,0,0,0,1,1,0,0,0]=>9
[1,1,1,1,0,0,1,0,0,0,1,0]=>14
[1,1,1,1,0,0,1,0,0,1,0,0]=>11
[1,1,1,1,0,0,1,0,1,0,0,0]=>8
[1,1,1,1,0,0,1,1,0,0,0,0]=>5
[1,1,1,1,0,1,0,0,0,0,1,0]=>10
[1,1,1,1,0,1,0,0,0,1,0,0]=>8
[1,1,1,1,0,1,0,0,1,0,0,0]=>6
[1,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[1,1,1,1,1,0,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>428
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>296
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>344
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>254
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>164
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>358
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>254
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>302
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>226
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>150
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>218
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>170
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>122
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>74
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>358
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>251
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>294
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>219
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>144
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>313
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>224
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>267
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>201
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>135
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>198
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>155
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>112
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>69
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>232
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>170
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>204
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>156
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>108
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>162
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>128
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>94
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>60
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>106
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>86
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>66
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>46
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>26
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>344
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>240
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>280
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>208
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>136
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>294
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>210
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>250
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>188
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>126
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>184
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>144
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>104
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>64
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>302
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>213
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>250
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>187
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>124
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>267
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>192
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>229
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>173
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>117
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>172
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>135
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>98
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>61
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>204
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>150
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>180
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>138
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>96
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>144
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>114
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>84
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>54
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>96
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>78
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>60
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>42
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>24
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>218
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>156
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>184
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>139
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>94
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>198
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>144
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>172
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>131
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>90
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>133
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>105
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>77
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>49
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>162
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>120
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>144
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>111
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>78
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>117
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>93
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>69
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>45
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>81
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>66
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>51
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>36
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>21
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>106
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>80
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>96
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>75
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>54
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>81
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>65
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>49
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>33
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>61
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>50
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>39
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>28
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>17
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>36
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>30
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>24
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>18
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>12
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>296
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>206
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>240
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>178
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>116
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>251
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>179
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>213
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>160
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>107
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>156
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>122
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>88
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>54
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>254
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>179
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>210
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>157
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>104
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>224
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>161
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>192
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>145
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>98
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>144
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>113
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>82
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>51
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>170
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>125
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>150
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>115
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>80
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>120
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>95
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>70
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>45
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>80
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>65
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>50
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>35
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>20
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>254
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>178
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>208
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>155
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>102
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>219
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>157
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>187
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>141
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>95
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>139
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>109
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>79
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>49
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>226
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>160
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>188
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>141
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>94
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>201
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>145
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>173
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>131
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>89
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>131
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>103
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>75
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>47
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>156
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>115
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>138
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>106
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>74
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>111
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>88
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>65
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>42
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>75
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>61
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>47
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>33
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>19
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>170
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>122
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>144
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>109
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>74
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>155
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>113
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>135
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>103
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>71
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>105
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>83
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>61
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>39
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>128
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>95
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>114
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>88
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>62
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>93
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>74
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>55
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>36
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>65
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>53
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>41
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>29
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>17
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>86
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>65
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>78
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>61
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>44
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>66
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>53
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>40
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>27
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>50
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>41
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>32
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>23
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>14
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>30
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>25
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>20
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>15
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>10
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>164
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>116
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>136
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>102
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>68
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>144
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>104
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>124
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>94
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>64
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>94
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>74
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>54
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>34
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>150
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>107
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>126
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>95
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>64
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>135
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>98
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>117
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>89
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>61
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>90
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>71
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>52
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>33
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>108
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>80
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>96
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>74
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>52
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>78
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>62
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>46
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>30
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>54
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>44
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>34
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>24
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>14
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>122
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>88
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>104
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>79
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>54
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>112
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>82
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>98
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>75
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>52
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>77
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>61
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>45
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>29
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>94
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>70
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>84
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>65
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>46
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>69
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>55
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>41
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>27
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>49
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>40
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>31
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>22
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>13
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>66
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>50
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>60
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>47
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>34
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>51
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>41
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>31
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>21
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>39
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>32
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>25
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>18
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>11
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>24
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>20
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>16
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>12
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>8
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>74
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>54
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>64
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>49
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>34
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>69
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>51
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>61
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>47
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>33
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>49
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>39
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>29
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>19
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>60
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>45
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>54
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>42
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>30
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>45
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>36
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>27
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>18
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>33
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>27
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>21
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>15
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>9
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>46
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>35
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>42
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>33
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>24
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>36
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>29
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>22
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>15
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>28
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>23
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>18
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>13
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>8
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>18
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>15
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>12
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>9
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>6
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>26
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>20
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>24
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>19
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>14
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>21
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>17
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>13
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>9
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>17
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>14
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>11
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>8
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>12
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>10
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>8
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>6
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>4
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1429
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1000
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1165
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>868
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>571
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1219
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>874
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1039
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>784
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>529
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>769
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>604
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>439
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>274
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1233
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>874
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>1025
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>770
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>515
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1093
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>790
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>941
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>714
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>487
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>713
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>562
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>411
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>260
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>841
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>622
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>745
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>574
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>403
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>601
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>478
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>355
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>232
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>409
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>334
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>259
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>184
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>109
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1219
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>860
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>1005
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>753
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>501
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>1059
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>764
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>909
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>689
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>469
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>684
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>539
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>394
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>249
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1093
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>779
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>915
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>690
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>465
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>978
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>710
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>846
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>644
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>442
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>648
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>512
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>376
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>240
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>771
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>572
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>685
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>529
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>373
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>556
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>443
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>330
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>217
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>384
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>314
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>244
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>174
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>104
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>841
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>608
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>717
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>546
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>375
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>771
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>566
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>675
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>518
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>361
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>531
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>422
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>313
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>204
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>645
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>482
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>577
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>448
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>319
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>475
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>380
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>285
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>190
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>339
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>278
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>217
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>156
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>95
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>449
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>342
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>409
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>322
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>235
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>349
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>282
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>215
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>148
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>269
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>222
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>175
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>128
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>81
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>169
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>142
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>115
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>88
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>61
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>34
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1165
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>820
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>957
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>716
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>475
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>1005
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>724
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>861
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>652
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>443
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>645
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>508
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>371
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>234
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>1025
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>730
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>857
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>646
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>435
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>915
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>664
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>791
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>602
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>413
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>605
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>478
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>351
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>224
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>717
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>532
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>637
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>492
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>347
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>517
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>412
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>307
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>202
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>357
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>292
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>227
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>162
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>97
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1039
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>736
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>861
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>647
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>433
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>909
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>658
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>783
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>595
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>407
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>594
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>469
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>344
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>219
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>941
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>673
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>791
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>598
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>405
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>846
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>616
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>734
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>560
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>386
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>566
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>448
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>330
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>212
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>675
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>502
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>601
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>465
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>329
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>490
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>391
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>292
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>193
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>342
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>280
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>218
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>156
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>94
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>745
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>540
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>637
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>486
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>335
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>685
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>504
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>601
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>462
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>323
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>475
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>378
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>281
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>184
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>577
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>432
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>517
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>402
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>287
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>427
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>342
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>257
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>172
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>307
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>252
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>197
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>142
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>87
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>409
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>312
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>373
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>294
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>215
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>319
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>258
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>197
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>136
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>247
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>204
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>161
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>118
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>75
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>157
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>132
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>107
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>82
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>57
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>32
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>769
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>550
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>645
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>488
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>331
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>684
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>499
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>594
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>454
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>314
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>459
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>364
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>269
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>174
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>713
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>514
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>605
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>460
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>315
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>648
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>475
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>566
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>434
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>302
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>443
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>352
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>261
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>170
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>531
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>397
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>475
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>369
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>263
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>391
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>313
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>235
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>157
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>279
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>229
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>179
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>129
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>79
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>601
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>438
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>517
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>396
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>275
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>556
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>411
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>490
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>378
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>266
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>391
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>312
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>233
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>154
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>475
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>357
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>427
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>333
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>239
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>355
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>285
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>215
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>145
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>259
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>213
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>167
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>121
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>75
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>349
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>267
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>319
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>252
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>185
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>274
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>222
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>170
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>118
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>214
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>177
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>140
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>103
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>66
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>139
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>117
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>95
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>73
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>51
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>29
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>409
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>302
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>357
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>276
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>195
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>384
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>287
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>342
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>266
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>190
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>279
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>224
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>169
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>114
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>339
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>257
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>307
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>241
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>175
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>259
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>209
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>159
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>109
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>195
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>161
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>127
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>93
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>59
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>269
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>207
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>247
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>196
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>145
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>214
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>174
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>134
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>94
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>170
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>141
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>112
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>83
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>54
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>115
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>97
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>79
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>61
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>43
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>25
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>169
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>132
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>157
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>126
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>95
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>139
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>114
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>89
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>64
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>115
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>96
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>77
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>58
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>39
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>85
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>72
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>59
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>46
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>33
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>20
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>49
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>42
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>35
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>28
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>21
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>14
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1000
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>703
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>820
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>613
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>406
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>860
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>619
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>736
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>557
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>378
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>550
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>433
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>316
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>199
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>874
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>622
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>730
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>550
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>370
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>779
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>565
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>673
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>512
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>351
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>514
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>406
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>298
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>190
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>608
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>451
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>540
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>417
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>294
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>438
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>349
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>260
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>171
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>302
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>247
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>192
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>137
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>82
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>874
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>619
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>724
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>544
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>364
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>764
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>553
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>658
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>500
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>342
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>499
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>394
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>289
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>184
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>790
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>565
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>664
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>502
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>340
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>710
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>517
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>616
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>470
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>324
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>475
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>376
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>277
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>178
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>566
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>421
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>504
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>390
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>276
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>411
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>328
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>245
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>162
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>287
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>235
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>183
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>131
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>79
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>622
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>451
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>532
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>406
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>280
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>572
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>421
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>502
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>386
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>270
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>397
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>316
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>235
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>154
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>482
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>361
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>432
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>336
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>240
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>357
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>286
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>215
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>144
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>257
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>211
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>165
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>119
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>73
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>342
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>261
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>312
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>246
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>180
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>267
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>216
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>165
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>114
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>207
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>171
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>135
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>99
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>63
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>132
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>111
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>90
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>69
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>48
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>27
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>868
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>613
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>716
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>537
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>358
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>753
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>544
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>647
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>491
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>335
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>488
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>385
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>282
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>179
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>770
                    

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$F_{2} = 1 + q$

$F_{3} = 1 + q + 2\ q^{2} + q^{4}$

$F_{4} = 1 + q + 2\ q^{2} + 2\ q^{3} + q^{4} + q^{5} + 2\ q^{6} + 2\ q^{8} + q^{9} + q^{13}$

$F_{5} = 1 + q + 2\ q^{2} + 2\ q^{3} + 3\ q^{4} + q^{5} + 2\ q^{6} + 4\ q^{8} + 3\ q^{9} + 2\ q^{11} + 2\ q^{12} + 3\ q^{13} + 2\ q^{15} + q^{16} + 3\ q^{18} + 2\ q^{21} + 2\ q^{22} + q^{25} + 2\ q^{27} + 2\ q^{31} + q^{41}$

$F_{6} = 1 + q + 2\ q^{2} + 2\ q^{3} + 3\ q^{4} + 3\ q^{5} + 2\ q^{6} + 4\ q^{8} + 3\ q^{9} + 2\ q^{10} + 2\ q^{11} + 2\ q^{12} + 3\ q^{13} + 4\ q^{14} + 4\ q^{15} + q^{16} + 2\ q^{17} + 3\ q^{18} + 3\ q^{19} + 2\ q^{20} + 2\ q^{21} + 2\ q^{22} + 2\ q^{23} + 2\ q^{24} + 2\ q^{25} + 4\ q^{27} + 4\ q^{29} + 2\ q^{30} + 2\ q^{31} + 2\ q^{32} + 4\ q^{33} + 2\ q^{34} + 2\ q^{36} + 2\ q^{39} + 2\ q^{40} + 4\ q^{41} + 2\ q^{42} + 2\ q^{44} + q^{45} + 2\ q^{46} + 4\ q^{47} + 3\ q^{52} + 2\ q^{53} + 2\ q^{55} + 5\ q^{61} + 2\ q^{62} + 2\ q^{65} + 2\ q^{71} + 3\ q^{74} + 2\ q^{75} + q^{83} + 2\ q^{88} + 2\ q^{89} + 2\ q^{103} + q^{106} + q^{131}$

$F_{7} = 1 + q + 2\ q^{2} + 2\ q^{3} + 3\ q^{4} + 3\ q^{5} + 4\ q^{6} + 4\ q^{8} + 3\ q^{9} + 2\ q^{10} + 2\ q^{11} + 4\ q^{12} + 3\ q^{13} + 4\ q^{14} + 4\ q^{15} + q^{16} + 4\ q^{17} + 5\ q^{18} + 3\ q^{19} + 4\ q^{20} + 4\ q^{21} + 2\ q^{22} + 2\ q^{23} + 6\ q^{24} + 2\ q^{25} + 2\ q^{26} + 4\ q^{27} + 2\ q^{28} + 4\ q^{29} + 4\ q^{30} + 2\ q^{31} + 2\ q^{32} + 6\ q^{33} + 4\ q^{34} + 2\ q^{35} + 5\ q^{36} + 4\ q^{39} + 2\ q^{40} + 4\ q^{41} + 4\ q^{42} + 2\ q^{44} + 5\ q^{45} + 4\ q^{46} + 4\ q^{47} + 6\ q^{49} + 4\ q^{50} + 4\ q^{51} + 3\ q^{52} + 2\ q^{53} + 8\ q^{54} + 2\ q^{55} + 4\ q^{60} + 8\ q^{61} + 2\ q^{62} + 4\ q^{64} + 6\ q^{65} + 4\ q^{66} + q^{68} + 4\ q^{69} + 2\ q^{70} + 2\ q^{71} + 7\ q^{74} + 4\ q^{75} + 2\ q^{77} + 4\ q^{78} + 2\ q^{79} + 4\ q^{80} + 2\ q^{81} + 2\ q^{82} + q^{83} + 2\ q^{84} + 2\ q^{86} + 4\ q^{88} + 2\ q^{89} + 2\ q^{90} + 2\ q^{93} + 6\ q^{94} + 4\ q^{95} + 4\ q^{96} + 4\ q^{98} + 2\ q^{102} + 2\ q^{103} + 4\ q^{104} + 2\ q^{105} + 3\ q^{106} + 2\ q^{107} + 2\ q^{108} + 2\ q^{109} + 2\ q^{111} + 2\ q^{112} + 2\ q^{113} + 2\ q^{114} + 2\ q^{115} + 2\ q^{116} + 3\ q^{117} + 2\ q^{120} + 4\ q^{122} + 2\ q^{124} + q^{125} + 2\ q^{126} + 2\ q^{128} + 3\ q^{131} + q^{133} + 4\ q^{135} + 2\ q^{136} + 2\ q^{138} + 2\ q^{139} + 2\ q^{141} + 8\ q^{144} + 2\ q^{145} + 4\ q^{150} + 3\ q^{155} + 4\ q^{156} + 2\ q^{157} + 2\ q^{160} + q^{161} + 2\ q^{162} + 2\ q^{164} + 4\ q^{170} + 2\ q^{172} + 2\ q^{173} + 2\ q^{178} + 2\ q^{179} + q^{180} + 2\ q^{184} + 2\ q^{187} + 2\ q^{188} + 2\ q^{192} + 2\ q^{198} + 2\ q^{201} + 2\ q^{204} + q^{206} + 2\ q^{208} + 2\ q^{210} + 2\ q^{213} + 2\ q^{218} + 2\ q^{219} + 2\ q^{224} + 2\ q^{226} + q^{229} + q^{232} + 2\ q^{240} + 2\ q^{250} + 2\ q^{251} + 4\ q^{254} + 2\ q^{267} + q^{280} + 2\ q^{294} + 2\ q^{296} + 2\ q^{302} + q^{313} + 2\ q^{344} + 2\ q^{358} + q^{428}$

Description

The number of Dyck paths that are weakly above the Dyck path, except for the path itself.

Code

def contains(A,B):
     Aa = A.to_area_sequence()
     Bb = B.to_area_sequence()
     return all( Aa[i] >= Bb[i] for i in range(len(Aa)) )

def statistic(D):
    n = len(D)/2
    return sum( 1 for A in DyckWords(n) if contains(A,D) ) - 1

Created

Feb 26, 2016 at 10:42 by Christian Stump

Updated

Nov 16, 2017 at 11:43 by Martin Rubey