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Identifier

St000420: Dyck paths ⟶ ℤ (values match St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself.)

Values

=>
                            Cc0005;cc-rep
                            
                            
                            

                        [1,0,1,0]=>2
[1,1,0,0]=>1
[1,0,1,0,1,0]=>5
[1,0,1,1,0,0]=>3
[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]=>14
[1,0,1,0,1,1,0,0]=>9
[1,0,1,1,0,0,1,0]=>10
[1,0,1,1,0,1,0,0]=>7
[1,0,1,1,1,0,0,0]=>4
[1,1,0,0,1,0,1,0]=>9
[1,1,0,0,1,1,0,0]=>6
[1,1,0,1,0,0,1,0]=>7
[1,1,0,1,0,1,0,0]=>5
[1,1,0,1,1,0,0,0]=>3
[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]=>42
[1,0,1,0,1,0,1,1,0,0]=>28
[1,0,1,0,1,1,0,0,1,0]=>32
[1,0,1,0,1,1,0,1,0,0]=>23
[1,0,1,0,1,1,1,0,0,0]=>14
[1,0,1,1,0,0,1,0,1,0]=>32
[1,0,1,1,0,0,1,1,0,0]=>22
[1,0,1,1,0,1,0,0,1,0]=>26
[1,0,1,1,0,1,0,1,0,0]=>19
[1,0,1,1,0,1,1,0,0,0]=>12
[1,0,1,1,1,0,0,0,1,0]=>17
[1,0,1,1,1,0,0,1,0,0]=>13
[1,0,1,1,1,0,1,0,0,0]=>9
[1,0,1,1,1,1,0,0,0,0]=>5
[1,1,0,0,1,0,1,0,1,0]=>28
[1,1,0,0,1,0,1,1,0,0]=>19
[1,1,0,0,1,1,0,0,1,0]=>22
[1,1,0,0,1,1,0,1,0,0]=>16
[1,1,0,0,1,1,1,0,0,0]=>10
[1,1,0,1,0,0,1,0,1,0]=>23
[1,1,0,1,0,0,1,1,0,0]=>16
[1,1,0,1,0,1,0,0,1,0]=>19
[1,1,0,1,0,1,0,1,0,0]=>14
[1,1,0,1,0,1,1,0,0,0]=>9
[1,1,0,1,1,0,0,0,1,0]=>13
[1,1,0,1,1,0,0,1,0,0]=>10
[1,1,0,1,1,0,1,0,0,0]=>7
[1,1,0,1,1,1,0,0,0,0]=>4
[1,1,1,0,0,0,1,0,1,0]=>14
[1,1,1,0,0,0,1,1,0,0]=>10
[1,1,1,0,0,1,0,0,1,0]=>12
[1,1,1,0,0,1,0,1,0,0]=>9
[1,1,1,0,0,1,1,0,0,0]=>6
[1,1,1,0,1,0,0,0,1,0]=>9
[1,1,1,0,1,0,0,1,0,0]=>7
[1,1,1,0,1,0,1,0,0,0]=>5
[1,1,1,0,1,1,0,0,0,0]=>3
[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]=>132
[1,0,1,0,1,0,1,0,1,1,0,0]=>90
[1,0,1,0,1,0,1,1,0,0,1,0]=>104
[1,0,1,0,1,0,1,1,0,1,0,0]=>76
[1,0,1,0,1,0,1,1,1,0,0,0]=>48
[1,0,1,0,1,1,0,0,1,0,1,0]=>107
[1,0,1,0,1,1,0,0,1,1,0,0]=>75
[1,0,1,0,1,1,0,1,0,0,1,0]=>89
[1,0,1,0,1,1,0,1,0,1,0,0]=>66
[1,0,1,0,1,1,0,1,1,0,0,0]=>43
[1,0,1,0,1,1,1,0,0,0,1,0]=>62
[1,0,1,0,1,1,1,0,0,1,0,0]=>48
[1,0,1,0,1,1,1,0,1,0,0,0]=>34
[1,0,1,0,1,1,1,1,0,0,0,0]=>20
[1,0,1,1,0,0,1,0,1,0,1,0]=>104
[1,0,1,1,0,0,1,0,1,1,0,0]=>72
[1,0,1,1,0,0,1,1,0,0,1,0]=>84
[1,0,1,1,0,0,1,1,0,1,0,0]=>62
[1,0,1,1,0,0,1,1,1,0,0,0]=>40
[1,0,1,1,0,1,0,0,1,0,1,0]=>89
[1,0,1,1,0,1,0,0,1,1,0,0]=>63
[1,0,1,1,0,1,0,1,0,0,1,0]=>75
[1,0,1,1,0,1,0,1,0,1,0,0]=>56
[1,0,1,1,0,1,0,1,1,0,0,0]=>37
[1,0,1,1,0,1,1,0,0,0,1,0]=>54
[1,0,1,1,0,1,1,0,0,1,0,0]=>42
[1,0,1,1,0,1,1,0,1,0,0,0]=>30
[1,0,1,1,0,1,1,1,0,0,0,0]=>18
[1,0,1,1,1,0,0,0,1,0,1,0]=>62
[1,0,1,1,1,0,0,0,1,1,0,0]=>45
[1,0,1,1,1,0,0,1,0,0,1,0]=>54
[1,0,1,1,1,0,0,1,0,1,0,0]=>41
[1,0,1,1,1,0,0,1,1,0,0,0]=>28
[1,0,1,1,1,0,1,0,0,0,1,0]=>42
[1,0,1,1,1,0,1,0,0,1,0,0]=>33
[1,0,1,1,1,0,1,0,1,0,0,0]=>24
[1,0,1,1,1,0,1,1,0,0,0,0]=>15
[1,0,1,1,1,1,0,0,0,0,1,0]=>26
[1,0,1,1,1,1,0,0,0,1,0,0]=>21
[1,0,1,1,1,1,0,0,1,0,0,0]=>16
[1,0,1,1,1,1,0,1,0,0,0,0]=>11
[1,0,1,1,1,1,1,0,0,0,0,0]=>6
[1,1,0,0,1,0,1,0,1,0,1,0]=>90
[1,1,0,0,1,0,1,0,1,1,0,0]=>62
[1,1,0,0,1,0,1,1,0,0,1,0]=>72
[1,1,0,0,1,0,1,1,0,1,0,0]=>53
[1,1,0,0,1,0,1,1,1,0,0,0]=>34
[1,1,0,0,1,1,0,0,1,0,1,0]=>75
[1,1,0,0,1,1,0,0,1,1,0,0]=>53
[1,1,0,0,1,1,0,1,0,0,1,0]=>63
[1,1,0,0,1,1,0,1,0,1,0,0]=>47
[1,1,0,0,1,1,0,1,1,0,0,0]=>31
[1,1,0,0,1,1,1,0,0,0,1,0]=>45
[1,1,0,0,1,1,1,0,0,1,0,0]=>35
[1,1,0,0,1,1,1,0,1,0,0,0]=>25
[1,1,0,0,1,1,1,1,0,0,0,0]=>15
[1,1,0,1,0,0,1,0,1,0,1,0]=>76
[1,1,0,1,0,0,1,0,1,1,0,0]=>53
[1,1,0,1,0,0,1,1,0,0,1,0]=>62
[1,1,0,1,0,0,1,1,0,1,0,0]=>46
[1,1,0,1,0,0,1,1,1,0,0,0]=>30
[1,1,0,1,0,1,0,0,1,0,1,0]=>66
[1,1,0,1,0,1,0,0,1,1,0,0]=>47
[1,1,0,1,0,1,0,1,0,0,1,0]=>56
[1,1,0,1,0,1,0,1,0,1,0,0]=>42
[1,1,0,1,0,1,0,1,1,0,0,0]=>28
[1,1,0,1,0,1,1,0,0,0,1,0]=>41
[1,1,0,1,0,1,1,0,0,1,0,0]=>32
[1,1,0,1,0,1,1,0,1,0,0,0]=>23
[1,1,0,1,0,1,1,1,0,0,0,0]=>14
[1,1,0,1,1,0,0,0,1,0,1,0]=>48
[1,1,0,1,1,0,0,0,1,1,0,0]=>35
[1,1,0,1,1,0,0,1,0,0,1,0]=>42
[1,1,0,1,1,0,0,1,0,1,0,0]=>32
[1,1,0,1,1,0,0,1,1,0,0,0]=>22
[1,1,0,1,1,0,1,0,0,0,1,0]=>33
[1,1,0,1,1,0,1,0,0,1,0,0]=>26
[1,1,0,1,1,0,1,0,1,0,0,0]=>19
[1,1,0,1,1,0,1,1,0,0,0,0]=>12
[1,1,0,1,1,1,0,0,0,0,1,0]=>21
[1,1,0,1,1,1,0,0,0,1,0,0]=>17
[1,1,0,1,1,1,0,0,1,0,0,0]=>13
[1,1,0,1,1,1,0,1,0,0,0,0]=>9
[1,1,0,1,1,1,1,0,0,0,0,0]=>5
[1,1,1,0,0,0,1,0,1,0,1,0]=>48
[1,1,1,0,0,0,1,0,1,1,0,0]=>34
[1,1,1,0,0,0,1,1,0,0,1,0]=>40
[1,1,1,0,0,0,1,1,0,1,0,0]=>30
[1,1,1,0,0,0,1,1,1,0,0,0]=>20
[1,1,1,0,0,1,0,0,1,0,1,0]=>43
[1,1,1,0,0,1,0,0,1,1,0,0]=>31
[1,1,1,0,0,1,0,1,0,0,1,0]=>37
[1,1,1,0,0,1,0,1,0,1,0,0]=>28
[1,1,1,0,0,1,0,1,1,0,0,0]=>19
[1,1,1,0,0,1,1,0,0,0,1,0]=>28
[1,1,1,0,0,1,1,0,0,1,0,0]=>22
[1,1,1,0,0,1,1,0,1,0,0,0]=>16
[1,1,1,0,0,1,1,1,0,0,0,0]=>10
[1,1,1,0,1,0,0,0,1,0,1,0]=>34
[1,1,1,0,1,0,0,0,1,1,0,0]=>25
[1,1,1,0,1,0,0,1,0,0,1,0]=>30
[1,1,1,0,1,0,0,1,0,1,0,0]=>23
[1,1,1,0,1,0,0,1,1,0,0,0]=>16
[1,1,1,0,1,0,1,0,0,0,1,0]=>24
[1,1,1,0,1,0,1,0,0,1,0,0]=>19
[1,1,1,0,1,0,1,0,1,0,0,0]=>14
[1,1,1,0,1,0,1,1,0,0,0,0]=>9
[1,1,1,0,1,1,0,0,0,0,1,0]=>16
[1,1,1,0,1,1,0,0,0,1,0,0]=>13
[1,1,1,0,1,1,0,0,1,0,0,0]=>10
[1,1,1,0,1,1,0,1,0,0,0,0]=>7
[1,1,1,0,1,1,1,0,0,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,0]=>20
[1,1,1,1,0,0,0,0,1,1,0,0]=>15
[1,1,1,1,0,0,0,1,0,0,1,0]=>18
[1,1,1,1,0,0,0,1,0,1,0,0]=>14
[1,1,1,1,0,0,0,1,1,0,0,0]=>10
[1,1,1,1,0,0,1,0,0,0,1,0]=>15
[1,1,1,1,0,0,1,0,0,1,0,0]=>12
[1,1,1,1,0,0,1,0,1,0,0,0]=>9
[1,1,1,1,0,0,1,1,0,0,0,0]=>6
[1,1,1,1,0,1,0,0,0,0,1,0]=>11
[1,1,1,1,0,1,0,0,0,1,0,0]=>9
[1,1,1,1,0,1,0,0,1,0,0,0]=>7
[1,1,1,1,0,1,0,1,0,0,0,0]=>5
[1,1,1,1,0,1,1,0,0,0,0,0]=>3
[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]=>429
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>297
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>345
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>255
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>165
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>359
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>255
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>303
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>227
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>151
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>219
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>171
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>123
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>75
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>359
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>252
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>295
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>220
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>145
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>314
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>225
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>268
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>202
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>136
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>199
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>156
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>113
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>70
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>233
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>171
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>205
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>157
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>109
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>163
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>129
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>95
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>61
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>107
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>87
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>67
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>47
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>27
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>345
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>241
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>281
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>209
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>137
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>295
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>211
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>251
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>189
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>127
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>185
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>145
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>105
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>65
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>303
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>214
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>251
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>188
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>125
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>268
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>193
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>230
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>174
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>118
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>173
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>136
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>99
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>62
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>205
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>151
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>181
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>139
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>97
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>145
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>115
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>85
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>55
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>97
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>79
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>61
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>43
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>25
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>219
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>157
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>185
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>140
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>95
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>199
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>145
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>173
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>132
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>91
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>134
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>106
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>78
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>50
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>163
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>121
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>145
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>112
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>79
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>118
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>94
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>70
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>46
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>82
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>67
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>52
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>37
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>22
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>107
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>81
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>97
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>76
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>55
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>82
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>66
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>50
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>34
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>62
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>51
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>40
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>29
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>18
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>37
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>31
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>25
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>19
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>13
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>297
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>207
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>241
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>179
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>117
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>252
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>180
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>214
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>161
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>108
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>157
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>123
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>89
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>55
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>255
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>180
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>211
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>158
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>105
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>225
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>162
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>193
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>146
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>99
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>145
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>114
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>83
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>52
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>171
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>126
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>151
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>116
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>81
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>121
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>96
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>71
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>46
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>81
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>66
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>51
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>36
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>21
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>255
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>179
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>209
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>156
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>103
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>220
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>158
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>188
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>142
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>96
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>140
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>110
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>80
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>50
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>227
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>161
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>189
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>142
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>95
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>202
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>146
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>174
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>132
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>90
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>132
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>104
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>76
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>48
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>157
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>116
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>139
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>107
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>75
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>112
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>89
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>66
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>43
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>76
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>62
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>48
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>34
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>20
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>171
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>123
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>145
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>110
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>75
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>156
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>114
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>136
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>104
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>72
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>106
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>84
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>62
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>40
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>129
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>96
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>115
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>89
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>63
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>94
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>75
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>56
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>37
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>66
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>54
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>42
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>30
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>18
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>87
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>66
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>79
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>62
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>45
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>67
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>54
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>41
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>28
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>51
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>42
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>33
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>24
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>15
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>31
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>26
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>21
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>16
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>11
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>165
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>117
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>137
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>103
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>69
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>145
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>105
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>125
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>95
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>65
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>95
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>75
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>55
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>35
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>151
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>108
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>127
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>96
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>65
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>136
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>99
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>118
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>90
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>62
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>91
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>72
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>53
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>34
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>109
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>81
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>97
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>75
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>53
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>79
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>63
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>47
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>31
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>55
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>45
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>35
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>25
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>15
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>123
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>89
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>105
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>80
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>55
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>113
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>83
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>99
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>76
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>53
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>78
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>62
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>46
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>30
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>95
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>71
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>85
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>66
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>47
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>70
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>56
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>42
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>28
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>50
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>41
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>32
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>23
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>14
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>67
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>51
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>61
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>48
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>35
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>52
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>42
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>32
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>22
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>40
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>33
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>26
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>19
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>12
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>25
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>21
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>17
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>13
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>9
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>5
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>75
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>55
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>65
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>50
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>35
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>70
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>52
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>62
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>48
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>34
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>50
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>40
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>30
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>20
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>61
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>46
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>55
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>43
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>31
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>46
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>37
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>28
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>19
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>34
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>28
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>22
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>16
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>10
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>47
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>36
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>43
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>34
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>25
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>37
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>30
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>23
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>16
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>29
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>24
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>19
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>14
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>9
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>19
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>16
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>13
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>10
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>7
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>27
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>21
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>25
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>20
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>15
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>22
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>18
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>14
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>10
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>18
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>15
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>12
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>9
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>6
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>13
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>11
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>9
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>7
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>3
[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]=>1430
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1001
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1166
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>869
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>572
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1220
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>875
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1040
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>785
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>530
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>770
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>605
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>440
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>275
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1234
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>875
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>1026
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>771
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>516
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1094
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>791
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>942
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>715
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>488
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>714
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>563
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>412
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>261
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>842
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>623
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>746
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>575
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>404
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>602
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>479
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>356
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>233
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>410
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>335
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>260
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>185
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>110
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1220
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>861
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>1006
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>754
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>502
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>1060
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>765
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>910
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>690
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>470
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>685
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>540
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>395
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>250
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1094
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>780
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>916
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>691
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>466
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>979
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>711
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>847
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>645
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>443
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>649
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>513
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>377
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>241
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>772
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>573
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>686
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>530
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>374
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>557
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>444
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>331
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>218
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>385
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>315
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>245
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>175
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>105
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>842
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>609
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>718
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>547
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>376
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>772
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>567
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>676
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>519
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>362
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>532
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>423
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>314
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>205
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>646
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>483
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>578
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>449
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>320
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>476
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>381
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>286
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>191
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>340
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>279
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>218
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>157
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>96
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>450
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>343
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>410
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>323
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>236
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>350
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>283
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>216
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>149
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>270
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>223
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>176
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>129
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>82
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>170
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>143
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>116
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>89
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>62
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>35
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1166
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>821
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>958
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>717
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>476
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>1006
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>725
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>862
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>653
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>444
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>646
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>509
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>372
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>235
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>1026
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>731
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>858
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>647
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>436
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>916
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>665
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>792
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>603
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>414
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>606
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>479
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>352
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>225
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>718
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>533
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>638
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>493
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>348
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>518
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>413
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>308
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>203
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>358
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>293
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>228
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>163
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>98
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1040
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>737
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>862
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>648
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>434
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>910
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>659
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>784
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>596
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>408
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>595
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>470
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>345
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>220
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>942
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>674
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>792
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>599
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>406
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>847
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>617
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>735
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>561
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>387
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>567
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>449
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>331
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>213
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>676
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>503
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>602
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>466
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>330
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>491
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>392
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>293
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>194
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>343
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>281
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>219
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>157
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>95
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>746
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>541
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>638
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>487
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>336
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>686
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>505
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>602
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>463
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>324
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>476
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>379
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>282
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>185
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>578
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>433
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>518
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>403
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>288
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>428
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>343
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>258
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>173
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>308
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>253
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>198
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>143
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>88
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>410
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>313
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>374
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>295
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>216
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>320
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>259
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>198
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>137
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>248
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>205
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>162
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>119
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>76
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>158
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>133
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>108
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>83
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>58
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>33
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>770
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>551
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>646
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>489
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>332
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>685
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>500
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>595
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>455
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>315
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>460
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>365
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>270
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>175
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>714
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>515
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>606
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>461
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>316
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>649
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>476
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>567
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>435
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>303
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>444
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>353
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>262
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>171
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>532
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>398
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>476
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>370
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>264
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>392
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>314
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>236
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>158
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>280
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>230
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>180
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>130
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>80
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>602
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>439
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>518
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>397
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>276
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>557
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>412
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>491
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>379
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>267
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>392
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>313
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>234
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>155
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>476
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>358
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>428
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>334
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>240
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>356
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>286
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>216
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>146
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>260
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>214
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>168
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>122
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>76
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>350
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>268
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>320
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>253
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>186
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>275
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>223
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>171
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>119
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>215
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>178
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>141
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>104
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>67
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>140
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>118
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>96
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>74
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>52
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>30
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>410
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>303
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>358
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>277
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>196
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>385
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>288
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>343
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>267
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>191
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>280
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>225
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>170
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>115
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>340
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>258
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>308
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>242
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>176
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>260
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>210
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>160
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>110
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>196
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>162
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>128
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>94
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>60
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>270
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>208
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>248
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>197
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>146
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>215
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>175
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>135
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>95
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>171
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>142
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>113
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>84
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>55
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>116
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>98
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>80
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>62
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>44
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>26
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>170
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>133
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>158
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>127
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>96
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>140
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>115
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>90
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>65
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>116
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>97
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>78
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>59
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>40
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>86
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>73
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>60
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>47
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>34
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>21
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>50
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>43
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>36
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>29
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>22
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>15
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1001
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>704
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>821
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>614
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>407
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>861
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>620
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>737
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>558
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>379
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>551
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>434
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>317
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>200
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>875
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>623
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>731
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>551
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>371
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>780
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>566
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>674
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>513
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>352
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>515
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>407
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>299
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>191
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>609
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>452
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>541
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>418
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>295
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>439
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>350
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>261
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>172
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>303
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>248
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>193
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>138
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>83
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>875
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>620
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>725
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>545
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>365
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>765
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>554
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>659
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>501
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>343
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>500
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>395
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>290
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>185
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>791
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>566
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>665
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>503
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>341
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>711
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>518
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>617
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>471
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>325
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>476
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>377
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>278
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>179
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>567
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>422
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>505
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>391
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>277
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>412
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>329
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>246
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>163
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>288
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>236
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>184
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>132
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>80
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>623
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>452
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>533
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>407
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>281
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>573
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>422
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>503
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>387
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>271
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>398
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>317
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>236
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>155
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>483
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>362
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>433
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>337
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>241
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>358
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>287
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>216
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>145
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>258
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>212
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>166
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>120
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>74
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>343
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>262
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>313
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>247
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>181
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>268
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>217
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>166
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>115
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>208
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>172
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>136
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>100
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>64
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>133
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>112
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>91
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>70
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>49
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>28
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>869
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>614
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>717
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>538
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>359
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>754
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>545
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>648
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>492
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>336
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>489
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>386
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>283
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>180
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>771
                    

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

$F_{3} = q + q^{2} + 2\ q^{3} + q^{5}$

$F_{4} = q + q^{2} + 2\ q^{3} + 2\ q^{4} + q^{5} + q^{6} + 2\ q^{7} + 2\ q^{9} + q^{10} + q^{14}$

$F_{5} = q + q^{2} + 2\ q^{3} + 2\ q^{4} + 3\ q^{5} + q^{6} + 2\ q^{7} + 4\ q^{9} + 3\ q^{10} + 2\ q^{12} + 2\ q^{13} + 3\ q^{14} + 2\ q^{16} + q^{17} + 3\ q^{19} + 2\ q^{22} + 2\ q^{23} + q^{26} + 2\ q^{28} + 2\ q^{32} + q^{42}$

$F_{6} = q + q^{2} + 2\ q^{3} + 2\ q^{4} + 3\ q^{5} + 3\ q^{6} + 2\ q^{7} + 4\ q^{9} + 3\ q^{10} + 2\ q^{11} + 2\ q^{12} + 2\ q^{13} + 3\ q^{14} + 4\ q^{15} + 4\ q^{16} + q^{17} + 2\ q^{18} + 3\ q^{19} + 3\ q^{20} + 2\ q^{21} + 2\ q^{22} + 2\ q^{23} + 2\ q^{24} + 2\ q^{25} + 2\ q^{26} + 4\ q^{28} + 4\ q^{30} + 2\ q^{31} + 2\ q^{32} + 2\ q^{33} + 4\ q^{34} + 2\ q^{35} + 2\ q^{37} + 2\ q^{40} + 2\ q^{41} + 4\ q^{42} + 2\ q^{43} + 2\ q^{45} + q^{46} + 2\ q^{47} + 4\ q^{48} + 3\ q^{53} + 2\ q^{54} + 2\ q^{56} + 5\ q^{62} + 2\ q^{63} + 2\ q^{66} + 2\ q^{72} + 3\ q^{75} + 2\ q^{76} + q^{84} + 2\ q^{89} + 2\ q^{90} + 2\ q^{104} + q^{107} + q^{132}$

$F_{7} = q + q^{2} + 2\ q^{3} + 2\ q^{4} + 3\ q^{5} + 3\ q^{6} + 4\ q^{7} + 4\ q^{9} + 3\ q^{10} + 2\ q^{11} + 2\ q^{12} + 4\ q^{13} + 3\ q^{14} + 4\ q^{15} + 4\ q^{16} + q^{17} + 4\ q^{18} + 5\ q^{19} + 3\ q^{20} + 4\ q^{21} + 4\ q^{22} + 2\ q^{23} + 2\ q^{24} + 6\ q^{25} + 2\ q^{26} + 2\ q^{27} + 4\ q^{28} + 2\ q^{29} + 4\ q^{30} + 4\ q^{31} + 2\ q^{32} + 2\ q^{33} + 6\ q^{34} + 4\ q^{35} + 2\ q^{36} + 5\ q^{37} + 4\ q^{40} + 2\ q^{41} + 4\ q^{42} + 4\ q^{43} + 2\ q^{45} + 5\ q^{46} + 4\ q^{47} + 4\ q^{48} + 6\ q^{50} + 4\ q^{51} + 4\ q^{52} + 3\ q^{53} + 2\ q^{54} + 8\ q^{55} + 2\ q^{56} + 4\ q^{61} + 8\ q^{62} + 2\ q^{63} + 4\ q^{65} + 6\ q^{66} + 4\ q^{67} + q^{69} + 4\ q^{70} + 2\ q^{71} + 2\ q^{72} + 7\ q^{75} + 4\ q^{76} + 2\ q^{78} + 4\ q^{79} + 2\ q^{80} + 4\ q^{81} + 2\ q^{82} + 2\ q^{83} + q^{84} + 2\ q^{85} + 2\ q^{87} + 4\ q^{89} + 2\ q^{90} + 2\ q^{91} + 2\ q^{94} + 6\ q^{95} + 4\ q^{96} + 4\ q^{97} + 4\ q^{99} + 2\ q^{103} + 2\ q^{104} + 4\ q^{105} + 2\ q^{106} + 3\ q^{107} + 2\ q^{108} + 2\ q^{109} + 2\ q^{110} + 2\ q^{112} + 2\ q^{113} + 2\ q^{114} + 2\ q^{115} + 2\ q^{116} + 2\ q^{117} + 3\ q^{118} + 2\ q^{121} + 4\ q^{123} + 2\ q^{125} + q^{126} + 2\ q^{127} + 2\ q^{129} + 3\ q^{132} + q^{134} + 4\ q^{136} + 2\ q^{137} + 2\ q^{139} + 2\ q^{140} + 2\ q^{142} + 8\ q^{145} + 2\ q^{146} + 4\ q^{151} + 3\ q^{156} + 4\ q^{157} + 2\ q^{158} + 2\ q^{161} + q^{162} + 2\ q^{163} + 2\ q^{165} + 4\ q^{171} + 2\ q^{173} + 2\ q^{174} + 2\ q^{179} + 2\ q^{180} + q^{181} + 2\ q^{185} + 2\ q^{188} + 2\ q^{189} + 2\ q^{193} + 2\ q^{199} + 2\ q^{202} + 2\ q^{205} + q^{207} + 2\ q^{209} + 2\ q^{211} + 2\ q^{214} + 2\ q^{219} + 2\ q^{220} + 2\ q^{225} + 2\ q^{227} + q^{230} + q^{233} + 2\ q^{241} + 2\ q^{251} + 2\ q^{252} + 4\ q^{255} + 2\ q^{268} + q^{281} + 2\ q^{295} + 2\ q^{297} + 2\ q^{303} + q^{314} + 2\ q^{345} + 2\ q^{359} + q^{429}$

Description

The number of Dyck paths that are weakly above a Dyck path.

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) )

Created

Feb 26, 2016 at 10:36 by Christian Stump

Updated

Feb 26, 2016 at 10:36 by Christian Stump