Step | Hyp | Ref
| Expression |
1 | | efadd.4 |
. . . 4
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2 | | efadd.5 |
. . . 4
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3 | 1, 2 | addcld 7967 |
. . 3
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4 | | efadd.3 |
. . . 4
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n"     |
5 | 4 | efcvg 11658 |
. . 3
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)"   |
6 | 3, 5 | syl 14 |
. 2
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7 | | efadd.1 |
. . . . . 6
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8 | 7 | eftvalcn 11649 |
. . . . 5
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9 | 1, 8 | sylan 283 |
. . . 4
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10 | | absexp 11072 |
. . . . . . 7
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11 | 1, 10 | sylan 283 |
. . . . . 6
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12 | | faccl 10699 |
. . . . . . . 8
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13 | 12 | adantl 277 |
. . . . . . 7
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14 | | nnre 8915 |
. . . . . . . 8
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15 | | nnnn0 9172 |
. . . . . . . . 9
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16 | 15 | nn0ge0d 9221 |
. . . . . . . 8
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17 | 14, 16 | absidd 11160 |
. . . . . . 7
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18 | 13, 17 | syl 14 |
. . . . . 6
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19 | 11, 18 | oveq12d 5887 |
. . . . 5
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20 | | expcl 10524 |
. . . . . . 7
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("      |
21 | 1, 20 | sylan 283 |
. . . . . 6
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22 | 13 | nncnd 8922 |
. . . . . 6
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23 | 13 | nnap0d 8954 |
. . . . . 6
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24 | 21, 22, 23 | absdivapd 11188 |
. . . . 5
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25 | 1 | abscld 11174 |
. . . . . . 7
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26 | 25 | recnd 7976 |
. . . . . 6
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27 | | eqid 2177 |
. . . . . . 7
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28 | 27 | eftvalcn 11649 |
. . . . . 6
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29 | 26, 28 | sylan 283 |
. . . . 5
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30 | 19, 24, 29 | 3eqtr4rd 2221 |
. . . 4
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31 | | eftcl 11646 |
. . . . 5
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32 | 1, 31 | sylan 283 |
. . . 4
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33 | | efadd.2 |
. . . . . 6
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34 | 33 | eftvalcn 11649 |
. . . . 5
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35 | 2, 34 | sylan 283 |
. . . 4
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36 | | eftcl 11646 |
. . . . 5
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`"     |
37 | 2, 36 | sylan 283 |
. . . 4
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)"   |
38 | 4 | eftvalcn 11649 |
. . . . . 6
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("                  |
39 | 3, 38 | sylan 283 |
. . . . 5
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40 | 1 | adantr 276 |
. . . . . . . 8
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41 | 2 | adantr 276 |
. . . . . . . 8
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42 | | simpr 110 |
. . . . . . . 8
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43 | | binom 11476 |
. . . . . . . 8
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("                             |
44 | 40, 41, 42, 43 | syl3anc 1238 |
. . . . . . 7
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45 | 44 | oveq1d 5884 |
. . . . . 6
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46 | | 0zd 9254 |
. . . . . . . . 9
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47 | 42 | nn0zd 9362 |
. . . . . . . . 9
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48 | 46, 47 | fzfigd 10417 |
. . . . . . . 8
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49 | | faccl 10699 |
. . . . . . . . . 10
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50 | 49 | adantl 277 |
. . . . . . . . 9
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51 | 50 | nncnd 8922 |
. . . . . . . 8
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52 | | bccl2 10732 |
. . . . . . . . . . 11
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53 | 52 | adantl 277 |
. . . . . . . . . 10
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)"     |
54 | 53 | nncnd 8922 |
. . . . . . . . 9
             |
55 | 1 | ad2antrr 488 |
. . . . . . . . . . 11
           |
56 | | fznn0sub 10043 |
. . . . . . . . . . . 12
         |
57 | 56 | adantl 277 |
. . . . . . . . . . 11
             |
58 | 55, 57 | expcld 10639 |
. . . . . . . . . 10
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)"         |
59 | 2 | ad2antrr 488 |
. . . . . . . . . . 11
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)"   |
60 | | elfznn0 10100 |
. . . . . . . . . . . 12
       |
61 | 60 | adantl 277 |
. . . . . . . . . . 11
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)"   |
62 | 59, 61 | expcld 10639 |
. . . . . . . . . 10
               |
63 | 58, 62 | mulcld 7968 |
. . . . . . . . 9
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64 | 54, 63 | mulcld 7968 |
. . . . . . . 8
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j"     |
65 | 50 | nnap0d 8954 |
. . . . . . . 8
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66 | 48, 51, 64, 65 | fsumdivapc 11442 |
. . . . . . 7
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67 | 55, 61 | expcld 10639 |
. . . . . . . . . . 11
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68 | 61, 12 | syl 14 |
. . . . . . . . . . . 12
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`"    |
69 | 68 | nncnd 8922 |
. . . . . . . . . . 11
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)"       |
70 | 68 | nnap0d 8954 |
. . . . . . . . . . 11
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`"  #   |
71 | 67, 69, 70 | divclapd 8736 |
. . . . . . . . . 10
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72 | 33 | eftvalcn 11649 |
. . . . . . . . . . . 12
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)"    |
73 | 59, 57, 72 | syl2anc 411 |
. . . . . . . . . . 11
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("         |
74 | 59, 57 | expcld 10639 |
. . . . . . . . . . . 12
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)"         |
75 | | faccl 10699 |
. . . . . . . . . . . . . 14
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76 | 57, 75 | syl 14 |
. . . . . . . . . . . . 13
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`"      |
77 | 76 | nncnd 8922 |
. . . . . . . . . . . 12
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`"      |
78 | 76 | nnap0d 8954 |
. . . . . . . . . . . 12
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)"       #   |
79 | 74, 77, 78 | divclapd 8736 |
. . . . . . . . . . 11
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("               |
80 | 73, 79 | eqeltrd 2254 |
. . . . . . . . . 10
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)"         |
81 | 71, 80 | mulcld 7968 |
. . . . . . . . 9
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`"            |
82 | | oveq2 5877 |
. . . . . . . . . . 11
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("      |
83 | | fveq2 5511 |
. . . . . . . . . . 11
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`"            |
84 | 82, 83 | oveq12d 5887 |
. . . . . . . . . 10
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("           |
85 | | oveq2 5877 |
. . . . . . . . . . 11
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)"   |
86 | 85 | fveq2d 5515 |
. . . . . . . . . 10
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`"                |
87 | 84, 86 | oveq12d 5887 |
. . . . . . . . 9
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)"               |
88 | 46, 47, 81, 87 | fisumrev2 11438 |
. . . . . . . 8
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89 | 33 | eftvalcn 11649 |
. . . . . . . . . . . . . 14
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90 | 59, 61, 89 | syl2anc 411 |
. . . . . . . . . . . . 13
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91 | 90 | oveq2d 5885 |
. . . . . . . . . . . 12
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92 | 76, 68 | nnmulcld 8957 |
. . . . . . . . . . . . . . 15
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93 | 92 | nncnd 8922 |
. . . . . . . . . . . . . 14
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94 | 77, 69, 78, 70 | mulap0d 8604 |
. . . . . . . . . . . . . 14
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95 | 63, 93, 94 | divrecap2d 8740 |
. . . . . . . . . . . . 13
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96 | 58, 77, 62, 69, 78, 70 | divmuldivapd 8778 |
. . . . . . . . . . . . 13
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97 | | bcval2 10714 |
. . . . . . . . . . . . . . . . 17
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("         |
98 | 97 | adantl 277 |
. . . . . . . . . . . . . . . 16
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)"                       |
99 | 98 | oveq1d 5884 |
. . . . . . . . . . . . . . 15
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)"           |
100 | 51 | adantr 276 |
. . . . . . . . . . . . . . . . 17
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)"        #   |
102 | 100, 93, 100, 94, 101 | divdiv32apd 8762 |
. . . . . . . . . . . . . . . 16
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)"         |
103 | 100, 101 | dividapd 8732 |
. . . . . . . . . . . . . . . . 17
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)"             |
104 | 103 | oveq1d 5884 |
. . . . . . . . . . . . . . . 16
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`"      |
105 | 102, 104 | eqtrd 2210 |
. . . . . . . . . . . . . . 15
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)"                                   |
106 | 99, 105 | eqtrd 2210 |
. . . . . . . . . . . . . 14
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)"                         |
107 | 106 | oveq1d 5884 |
. . . . . . . . . . . . 13
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108 | 95, 96, 107 | 3eqtr4rd 2221 |
. . . . . . . . . . . 12
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109 | 91, 108 | eqtr4d 2213 |
. . . . . . . . . . 11
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110 | | nn0cn 9175 |
. . . . . . . . . . . . . . . . 17
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111 | 110 | ad2antlr 489 |
. . . . . . . . . . . . . . . 16
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112 | 111 | addid2d 8097 |
. . . . . . . . . . . . . . 15
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)"     |
113 | 112 | oveq1d 5884 |
. . . . . . . . . . . . . 14
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114 | 113 | oveq2d 5885 |
. . . . . . . . . . . . 13
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115 | 113 | fveq2d 5515 |
. . . . . . . . . . . . 13
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)"   |
116 | 114, 115 | oveq12d 5887 |
. . . . . . . . . . . 12
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)"                                   |
117 | 113 | oveq2d 5885 |
. . . . . . . . . . . . . 14
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)"             |
118 | | nn0cn 9175 |
. . . . . . . . . . . . . . . 16

  |
119 | 61, 118 | syl 14 |
. . . . . . . . . . . . . . 15
           |
120 | 111, 119 | nncand 8263 |
. . . . . . . . . . . . . 14
               |
121 | 117, 120 | eqtrd 2210 |
. . . . . . . . . . . . 13
                 |
122 | 121 | fveq2d 5515 |
. . . . . . . . . . . 12
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123 | 116, 122 | oveq12d 5887 |
. . . . . . . . . . 11
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124 | 54, 63, 100, 101 | div23apd 8774 |
. . . . . . . . . . 11
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)"         |
125 | 109, 123,
124 | 3eqtr4rd 2221 |
. . . . . . . . . 10
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126 | 125 | sumeq2dv 11360 |
. . . . . . . . 9
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)"     |
127 | | oveq2 5877 |
. . . . . . . . . . . . 13
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128 | 127 | oveq2d 5885 |
. . . . . . . . . . . 12
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("      |
129 | 127 | fveq2d 5515 |
. . . . . . . . . . . 12
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)"   |
130 | 128, 129 | oveq12d 5887 |
. . . . . . . . . . 11
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("       |
131 | 127 | oveq2d 5885 |
. . . . . . . . . . . 12
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132 | 131 | fveq2d 5515 |
. . . . . . . . . . 11
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("       |
133 | 130, 132 | oveq12d 5887 |
. . . . . . . . . 10
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)"               |
134 | 133 | cbvsumv 11353 |
. . . . . . . . 9
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("       |
135 | 126, 134 | eqtrdi 2226 |
. . . . . . . 8
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136 | 88, 135 | eqtr4d 2213 |
. . . . . . 7
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137 | 66, 136 | eqtr4d 2213 |
. . . . . 6
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138 | 45, 137 | eqtrd 2210 |
. . . . 5
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("              |
139 | 39, 138 | eqtrd 2210 |
. . . 4
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140 | 27 | efcllem 11651 |
. . . . 5
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141 | 26, 140 | syl 14 |
. . . 4
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("        |
142 | 33 | efcllem 11651 |
. . . . 5
     |
143 | 2, 142 | syl 14 |
. . . 4
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144 | 7 | efcllem 11651 |
. . . . 5
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145 | 1, 144 | syl 14 |
. . . 4
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146 | 9, 30, 32, 35, 37, 139, 141, 143, 145 | mertensabs 11529 |
. . 3
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sum_"       |
150 | 2, 149 | syl 14 |
. . . 4
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("                        |
152 | 146, 151 | breqtrrd 4028 |
. 2
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)"   |
153 | | climuni 11285 |
. 2
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154 | 6, 152, 153 | syl2anc 411 |
1
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