diff --git a/main.typ b/main.typ index 115c860..8700f4f 100644 --- a/main.typ +++ b/main.typ @@ -8,4 +8,6 @@ #pagebreak() #include "problems/problem12a.typ" #pagebreak() +#include "problems/problem12bprime.typ" +#pagebreak() #include "problems/problem12b.typ" diff --git a/pdfs/main.pdf b/pdfs/main.pdf index fc9534a..c6a7302 100644 --- a/pdfs/main.pdf +++ b/pdfs/main.pdf @@ -2,1395 +2,1662 @@ % 1 0 obj -<> +<> endobj 2 0 obj -</Dest 415 0 R>> +</Dest 501 0 R>> endobj 3 0 obj -</Dest 416 0 R>> +</Dest 502 0 R>> endobj 4 0 obj -</Dest 417 0 R>> +</Dest 503 0 R>> endobj 5 0 obj -</Dest 418 0 R>> +</Dest 504 0 R>> endobj 6 0 obj -</Dest 419 0 R>> +</Dest 505 0 R>> endobj 7 0 obj -</Dest 420 0 R>> +</Dest 506 0 R>> endobj 8 0 obj -</Dest 421 0 R>> +</Dest 507 0 R>> endobj 9 0 obj -</Dest 422 0 R>> +</Dest 508 0 R>> endobj 10 0 obj -</Dest 423 0 R>> +</Dest 509 0 R>> endobj 11 0 obj -</Dest 424 0 R>> +</Dest 510 0 R>> endobj 12 0 obj -</Dest 425 0 R>> +</Dest 511 0 R>> endobj 13 0 obj -</Dest 426 0 R>> +</Dest 512 0 R>> endobj 14 0 obj -</Dest 427 0 R>> +</Dest 513 0 R>> endobj 15 0 obj -<> +</Dest 514 0 R>> endobj 16 0 obj -<>/K[412 0 R]/ParentTree<>/ParentTreeNextKey 9>> +<> endobj 17 0 obj -[26 0 R 26 0 R 26 0 R 32 0 R 32 0 R 32 0 R 27 0 R 32 0 R 28 0 R 28 0 R 28 0 R 32 0 R 29 0 R 29 0 R 29 0 R 29 0 R 29 0 R 29 0 R 29 0 R 29 0 R 32 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 32 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 32 0 R 32 0 R 32 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 36 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 36 0 R 35 0 R 35 0 R 35 0 R 36 0 R 37 0 R 38 0 R 39 0 R 40 0 R 44 0 R 41 0 R 41 0 R 44 0 R 42 0 R 42 0 R 42 0 R 44 0 R 43 0 R 43 0 R 43 0 R 44 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 48 0 R 49 0 R 59 0 R 50 0 R 50 0 R 50 0 R 50 0 R 50 0 R 59 0 R 51 0 R 51 0 R 51 0 R 59 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 59 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 59 0 R 59 0 R 54 0 R 54 0 R 54 0 R 54 0 R 54 0 R 59 0 R 55 0 R 55 0 R 55 0 R 59 0 R 56 0 R 56 0 R 56 0 R 56 0 R 56 0 R 56 0 R 56 0 R 59 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 59 0 R 59 0 R 58 0 R 58 0 R 58 0 R 59 0 R 61 0 R 69 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 69 0 R 63 0 R 63 0 R 63 0 R 63 0 R 63 0 R 69 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 69 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 69 0 R 69 0 R 69 0 R 66 0 R 69 0 R 69 0 R 69 0 R 67 0 R 67 0 R 67 0 R 69 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 69 0 R 70 0 R 70 0 R 70 0 R 70 0 R 70 0 R 70 0 R 70 0 R 71 0 R 71 0 R 71 0 R 71 0 R 71 0 R 71 0 R 71 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 76 0 R 76 0 R 76 0 R 76 0 R 77 0 R 77 0 R 77 0 R 77 0 R 78 0 R 78 0 R 78 0 R 78 0 R 79 0 R 79 0 R 79 0 R 79 0 R 80 0 R 80 0 R 80 0 R 80 0 R 81 0 R 81 0 R 81 0 R 81 0 R 83 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 86 0 R 85 0 R 85 0 R 85 0 R 85 0 R 85 0 R 85 0 R 85 0 R 86 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 90 0 R 90 0 R 90 0 R 88 0 R 88 0 R 88 0 R 90 0 R 89 0 R 89 0 R 89 0 R 90 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 93 0 R 92 0 R 92 0 R 92 0 R 93 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 94 0 R 95 0 R] +<>/K[498 0 R]/ParentTree<>/ParentTreeNextKey 10>> endobj 18 0 obj -[96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 100 0 R 103 0 R 101 0 R 101 0 R 101 0 R 101 0 R 101 0 R 101 0 R 101 0 R 101 0 R 101 0 R 101 0 R 103 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 103 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 105 0 R 105 0 R 106 0 R 106 0 R 107 0 R 107 0 R 107 0 R 107 0 R 108 0 R 109 0 R 109 0 R 109 0 R 109 0 R 112 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 112 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 122 0 R 114 0 R 114 0 R 114 0 R 122 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 122 0 R 116 0 R 116 0 R 116 0 R 122 0 R 117 0 R 117 0 R 117 0 R 117 0 R 122 0 R 118 0 R 118 0 R 118 0 R 122 0 R 119 0 R 119 0 R 119 0 R 122 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 122 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 122 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 124 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 127 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 127 0 R 131 0 R 128 0 R 128 0 R 128 0 R 131 0 R 129 0 R 129 0 R 129 0 R 129 0 R 129 0 R 129 0 R 129 0 R 129 0 R 129 0 R 129 0 R 129 0 R 129 0 R 129 0 R 129 0 R 131 0 R 130 0 R 130 0 R 130 0 R 130 0 R 130 0 R 131 0 R 132 0 R 132 0 R 132 0 R 132 0 R 132 0 R 132 0 R 132 0 R 133 0 R 133 0 R 133 0 R 133 0 R 133 0 R 133 0 R 133 0 R 134 0 R 134 0 R 135 0 R 135 0 R 136 0 R 136 0 R 137 0 R 137 0 R 138 0 R 139 0 R 139 0 R 139 0 R 139 0 R 140 0 R 141 0 R 141 0 R 141 0 R 141 0 R 142 0 R 146 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 146 0 R 146 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 146 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 151 0 R 148 0 R 148 0 R 148 0 R 151 0 R 149 0 R 149 0 R 149 0 R 149 0 R 149 0 R 149 0 R 149 0 R 151 0 R 150 0 R 151 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R 153 0 R] +[28 0 R 28 0 R 28 0 R 34 0 R 34 0 R 34 0 R 29 0 R 34 0 R 30 0 R 30 0 R 30 0 R 34 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 34 0 R 32 0 R 32 0 R 32 0 R 32 0 R 32 0 R 34 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 34 0 R 34 0 R 34 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 38 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 38 0 R 37 0 R 37 0 R 37 0 R 38 0 R 39 0 R 40 0 R 41 0 R 42 0 R 46 0 R 43 0 R 43 0 R 46 0 R 44 0 R 44 0 R 44 0 R 46 0 R 45 0 R 45 0 R 45 0 R 46 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 50 0 R 51 0 R 61 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 61 0 R 53 0 R 53 0 R 53 0 R 61 0 R 54 0 R 54 0 R 54 0 R 54 0 R 54 0 R 54 0 R 54 0 R 61 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 55 0 R 61 0 R 61 0 R 56 0 R 56 0 R 56 0 R 56 0 R 56 0 R 61 0 R 57 0 R 57 0 R 57 0 R 61 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 61 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 61 0 R 61 0 R 60 0 R 60 0 R 60 0 R 61 0 R 63 0 R 71 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 71 0 R 65 0 R 65 0 R 65 0 R 65 0 R 65 0 R 71 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 66 0 R 71 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 71 0 R 71 0 R 71 0 R 68 0 R 71 0 R 71 0 R 71 0 R 69 0 R 69 0 R 69 0 R 71 0 R 70 0 R 70 0 R 70 0 R 70 0 R 70 0 R 70 0 R 70 0 R 71 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 73 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 75 0 R 76 0 R 76 0 R 76 0 R 76 0 R 76 0 R 76 0 R 76 0 R 77 0 R 77 0 R 77 0 R 77 0 R 77 0 R 77 0 R 77 0 R 78 0 R 78 0 R 78 0 R 78 0 R 79 0 R 79 0 R 79 0 R 79 0 R 80 0 R 80 0 R 80 0 R 80 0 R 81 0 R 81 0 R 81 0 R 81 0 R 82 0 R 82 0 R 82 0 R 82 0 R 83 0 R 83 0 R 83 0 R 83 0 R 85 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 86 0 R 88 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 88 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 92 0 R 92 0 R 92 0 R 90 0 R 90 0 R 90 0 R 92 0 R 91 0 R 91 0 R 91 0 R 92 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 93 0 R 95 0 R 94 0 R 94 0 R 94 0 R 95 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 96 0 R 97 0 R] endobj 19 0 obj -[155 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 155 0 R 156 0 R 157 0 R 157 0 R 157 0 R 157 0 R 157 0 R 157 0 R 157 0 R 157 0 R 157 0 R 157 0 R 157 0 R 157 0 R 157 0 R] +[98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 102 0 R 105 0 R 103 0 R 103 0 R 103 0 R 103 0 R 103 0 R 103 0 R 103 0 R 103 0 R 103 0 R 103 0 R 105 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 105 0 R 106 0 R 106 0 R 106 0 R 106 0 R 106 0 R 106 0 R 106 0 R 107 0 R 107 0 R 108 0 R 108 0 R 109 0 R 109 0 R 109 0 R 109 0 R 110 0 R 111 0 R 111 0 R 111 0 R 111 0 R 114 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 114 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 124 0 R 116 0 R 116 0 R 116 0 R 124 0 R 117 0 R 117 0 R 117 0 R 117 0 R 117 0 R 117 0 R 117 0 R 124 0 R 118 0 R 118 0 R 118 0 R 124 0 R 119 0 R 119 0 R 119 0 R 119 0 R 124 0 R 120 0 R 120 0 R 120 0 R 124 0 R 121 0 R 121 0 R 121 0 R 124 0 R 122 0 R 122 0 R 122 0 R 122 0 R 122 0 R 122 0 R 122 0 R 122 0 R 122 0 R 122 0 R 122 0 R 122 0 R 122 0 R 124 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 123 0 R 124 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 126 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 127 0 R 129 0 R 128 0 R 128 0 R 128 0 R 128 0 R 128 0 R 128 0 R 128 0 R 128 0 R 128 0 R 128 0 R 128 0 R 128 0 R 128 0 R 128 0 R 129 0 R 133 0 R 130 0 R 130 0 R 130 0 R 133 0 R 131 0 R 131 0 R 131 0 R 131 0 R 131 0 R 131 0 R 131 0 R 131 0 R 131 0 R 131 0 R 131 0 R 131 0 R 131 0 R 131 0 R 133 0 R 132 0 R 132 0 R 132 0 R 132 0 R 132 0 R 133 0 R 134 0 R 134 0 R 134 0 R 134 0 R 134 0 R 134 0 R 134 0 R 135 0 R 135 0 R 135 0 R 135 0 R 135 0 R 135 0 R 135 0 R 136 0 R 136 0 R 137 0 R 137 0 R 138 0 R 138 0 R 139 0 R 139 0 R 140 0 R 141 0 R 141 0 R 141 0 R 141 0 R 142 0 R 143 0 R 143 0 R 143 0 R 143 0 R 144 0 R 148 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 148 0 R 148 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 147 0 R 148 0 R 149 0 R 149 0 R 149 0 R 149 0 R 149 0 R 149 0 R 149 0 R 149 0 R 149 0 R 149 0 R 149 0 R 149 0 R 149 0 R 149 0 R 153 0 R 150 0 R 150 0 R 150 0 R 153 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 153 0 R 152 0 R 153 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 154 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R] endobj 20 0 obj -[158 0 R 158 0 R 158 0 R 159 0 R 160 0 R 161 0 R 161 0 R 161 0 R 161 0 R 161 0 R 161 0 R 161 0 R 162 0 R 163 0 R 163 0 R 163 0 R 163 0 R 163 0 R 163 0 R 163 0 R 163 0 R 163 0 R 163 0 R 163 0 R 163 0 R 164 0 R 164 0 R 165 0 R 166 0 R 167 0 R 167 0 R 167 0 R 167 0 R 167 0 R 167 0 R 167 0 R 167 0 R 167 0 R 167 0 R 167 0 R 167 0 R 168 0 R 169 0 R 170 0 R 171 0 R 171 0 R 171 0 R 171 0 R 171 0 R 172 0 R 173 0 R 177 0 R 174 0 R 174 0 R 174 0 R 174 0 R 174 0 R 174 0 R 174 0 R 174 0 R 174 0 R 174 0 R 177 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 175 0 R 177 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 178 0 R 180 0 R 179 0 R 180 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 181 0 R 184 0 R 182 0 R 184 0 R 183 0 R 184 0 R 188 0 R 185 0 R 185 0 R 185 0 R 185 0 R 185 0 R 185 0 R 185 0 R 185 0 R 185 0 R 185 0 R 185 0 R 185 0 R 185 0 R 185 0 R 185 0 R 188 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 186 0 R 188 0 R 188 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 188 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 190 0 R 194 0 R 191 0 R 191 0 R 191 0 R 194 0 R 192 0 R 192 0 R 192 0 R 192 0 R 194 0 R 193 0 R 193 0 R 193 0 R 193 0 R 194 0 R 197 0 R 195 0 R 195 0 R 195 0 R 195 0 R 195 0 R 195 0 R 195 0 R 197 0 R 196 0 R 196 0 R 196 0 R 197 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 198 0 R 201 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 201 0 R 200 0 R 200 0 R 200 0 R 201 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 202 0 R 205 0 R 203 0 R 205 0 R 204 0 R 204 0 R 204 0 R 205 0 R 206 0 R 206 0 R 206 0 R 206 0 R 206 0 R 206 0 R 206 0 R 206 0 R 206 0 R 206 0 R 206 0 R 206 0 R 206 0 R 206 0 R 206 0 R 206 0 R 206 0 R 206 0 R 206 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 207 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 210 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 212 0 R 213 0 R] +[157 0 R 156 0 R 156 0 R 156 0 R 156 0 R 156 0 R 156 0 R 156 0 R 156 0 R 156 0 R 156 0 R 156 0 R 156 0 R 156 0 R 157 0 R 158 0 R 159 0 R 159 0 R 159 0 R 159 0 R 159 0 R 159 0 R 159 0 R 159 0 R 159 0 R 159 0 R 159 0 R 159 0 R 159 0 R] endobj 21 0 obj -[214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 215 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 217 0 R 222 0 R 218 0 R 218 0 R 218 0 R 222 0 R 219 0 R 222 0 R 220 0 R 220 0 R 220 0 R 220 0 R 222 0 R 222 0 R 221 0 R 221 0 R 221 0 R 221 0 R 221 0 R 222 0 R 223 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 224 0 R 225 0 R 226 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 227 0 R 233 0 R 233 0 R 228 0 R 229 0 R 230 0 R 231 0 R 232 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R 234 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 235 0 R 236 0 R 237 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 238 0 R 243 0 R 243 0 R 239 0 R 240 0 R 241 0 R 242 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 243 0 R 244 0 R 245 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 246 0 R 247 0 R 250 0 R 248 0 R 248 0 R 248 0 R 250 0 R 249 0 R 250 0 R 250 0 R 252 0 R 251 0 R 252 0 R 253 0 R 255 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 254 0 R 255 0 R 256 0 R 256 0 R 256 0 R 256 0 R 256 0 R 256 0 R 256 0 R 256 0 R 256 0 R 256 0 R 256 0 R 256 0 R 256 0 R 256 0 R 256 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 257 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R] +[160 0 R 160 0 R 160 0 R 161 0 R 162 0 R 163 0 R 163 0 R 163 0 R 163 0 R 163 0 R 163 0 R 163 0 R 164 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 165 0 R 166 0 R 166 0 R 167 0 R 168 0 R 169 0 R 169 0 R 169 0 R 169 0 R 169 0 R 169 0 R 169 0 R 169 0 R 169 0 R 169 0 R 169 0 R 169 0 R 170 0 R 171 0 R 172 0 R 173 0 R 173 0 R 173 0 R 173 0 R 173 0 R 174 0 R 175 0 R 179 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 179 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 177 0 R 179 0 R 178 0 R 178 0 R 178 0 R 178 0 R 178 0 R 178 0 R 178 0 R 178 0 R 178 0 R 178 0 R 178 0 R 178 0 R 178 0 R 180 0 R 182 0 R 181 0 R 182 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 183 0 R 186 0 R 184 0 R 186 0 R 185 0 R 186 0 R 190 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 187 0 R 190 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 188 0 R 190 0 R 190 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 189 0 R 190 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 191 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 192 0 R 196 0 R 193 0 R 193 0 R 193 0 R 196 0 R 194 0 R 194 0 R 194 0 R 194 0 R 196 0 R 195 0 R 195 0 R 195 0 R 195 0 R 196 0 R 199 0 R 197 0 R 197 0 R 197 0 R 197 0 R 197 0 R 197 0 R 197 0 R 199 0 R 198 0 R 198 0 R 198 0 R 199 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 200 0 R 203 0 R 201 0 R 201 0 R 201 0 R 201 0 R 201 0 R 201 0 R 201 0 R 203 0 R 202 0 R 202 0 R 202 0 R 203 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 204 0 R 207 0 R 205 0 R 207 0 R 206 0 R 206 0 R 206 0 R 207 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 208 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 209 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 210 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 211 0 R 212 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 213 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 214 0 R 215 0 R] endobj 22 0 obj -[261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 266 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 266 0 R 265 0 R 266 0 R 267 0 R 271 0 R 268 0 R 268 0 R 268 0 R 271 0 R 269 0 R 269 0 R 269 0 R 269 0 R 269 0 R 271 0 R 270 0 R 270 0 R 270 0 R 270 0 R 270 0 R 271 0 R 271 0 R 272 0 R 272 0 R 272 0 R 272 0 R 272 0 R 272 0 R 272 0 R 272 0 R 272 0 R 272 0 R 272 0 R 272 0 R 272 0 R 272 0 R 274 0 R 273 0 R 273 0 R 273 0 R 273 0 R 273 0 R 273 0 R 273 0 R 273 0 R 273 0 R 273 0 R 273 0 R 273 0 R 273 0 R 273 0 R 273 0 R 274 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 276 0 R 277 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 279 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 282 0 R 281 0 R 281 0 R 281 0 R 281 0 R 281 0 R 282 0 R 283 0 R 283 0 R 283 0 R 283 0 R 283 0 R 283 0 R 283 0 R 283 0 R 283 0 R 283 0 R 283 0 R 283 0 R 285 0 R 284 0 R] +[216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 216 0 R 217 0 R 218 0 R 218 0 R 218 0 R 218 0 R 218 0 R 218 0 R 218 0 R 218 0 R 218 0 R 218 0 R 218 0 R 218 0 R 218 0 R 219 0 R 224 0 R 220 0 R 220 0 R 220 0 R 224 0 R 221 0 R 224 0 R 222 0 R 222 0 R 222 0 R 222 0 R 224 0 R 224 0 R 223 0 R 223 0 R 223 0 R 223 0 R 223 0 R 224 0 R 225 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 226 0 R 227 0 R 228 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 229 0 R 235 0 R 235 0 R 230 0 R 231 0 R 232 0 R 233 0 R 234 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 236 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 237 0 R 238 0 R 239 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 240 0 R 245 0 R 245 0 R 241 0 R 242 0 R 243 0 R 244 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 245 0 R 246 0 R 247 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 248 0 R 249 0 R 252 0 R 250 0 R 250 0 R 250 0 R 252 0 R 251 0 R 252 0 R 252 0 R 254 0 R 253 0 R 254 0 R 255 0 R 257 0 R 256 0 R 256 0 R 256 0 R 256 0 R 256 0 R 256 0 R 256 0 R 256 0 R 256 0 R 257 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 258 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 259 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 260 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 261 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R 262 0 R] endobj 23 0 obj -[286 0 R 287 0 R 288 0 R 289 0 R 290 0 R 290 0 R 290 0 R 290 0 R 290 0 R 291 0 R 291 0 R 291 0 R 291 0 R 292 0 R 293 0 R 294 0 R 295 0 R 295 0 R 295 0 R 295 0 R 295 0 R 295 0 R 295 0 R 295 0 R 295 0 R 296 0 R 297 0 R 297 0 R 297 0 R 297 0 R 297 0 R 297 0 R 297 0 R 297 0 R 297 0 R 297 0 R 297 0 R 297 0 R 297 0 R 297 0 R 298 0 R 299 0 R 299 0 R 299 0 R 300 0 R 300 0 R 300 0 R 301 0 R 301 0 R 301 0 R 301 0 R 301 0 R 302 0 R 303 0 R 304 0 R 305 0 R 306 0 R 307 0 R 308 0 R 309 0 R 310 0 R 318 0 R 311 0 R 311 0 R 311 0 R 318 0 R 312 0 R 318 0 R 313 0 R 313 0 R 313 0 R 313 0 R 313 0 R 313 0 R 313 0 R 313 0 R 313 0 R 313 0 R 313 0 R 313 0 R 313 0 R 313 0 R 313 0 R 313 0 R 318 0 R 314 0 R 314 0 R 314 0 R 318 0 R 315 0 R 315 0 R 315 0 R 315 0 R 315 0 R 315 0 R 315 0 R 315 0 R 315 0 R 315 0 R 315 0 R 315 0 R 315 0 R 315 0 R 315 0 R 315 0 R 315 0 R 315 0 R 315 0 R 318 0 R 318 0 R 316 0 R 318 0 R 317 0 R 318 0 R 319 0 R 322 0 R 320 0 R 320 0 R 320 0 R 320 0 R 320 0 R 320 0 R 320 0 R 320 0 R 322 0 R 321 0 R 321 0 R 321 0 R 322 0 R 326 0 R 323 0 R 326 0 R 324 0 R 324 0 R 324 0 R 324 0 R 324 0 R 324 0 R 324 0 R 324 0 R 324 0 R 326 0 R 325 0 R 325 0 R 325 0 R 325 0 R 325 0 R 325 0 R 325 0 R 325 0 R 325 0 R 326 0 R 329 0 R 327 0 R 327 0 R 327 0 R 329 0 R 328 0 R 328 0 R 328 0 R 328 0 R 328 0 R 328 0 R 328 0 R 328 0 R 328 0 R 328 0 R 328 0 R 328 0 R 328 0 R 329 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 330 0 R 332 0 R 331 0 R 331 0 R 331 0 R 331 0 R 331 0 R 331 0 R 331 0 R 331 0 R 331 0 R 331 0 R 331 0 R 331 0 R 331 0 R 332 0 R 334 0 R 334 0 R 334 0 R 334 0 R 334 0 R 334 0 R 334 0 R 334 0 R 333 0 R 334 0 R 334 0 R 335 0 R] +[263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 263 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 264 0 R 265 0 R 265 0 R 265 0 R 265 0 R 265 0 R 265 0 R 265 0 R 265 0 R 265 0 R 265 0 R 265 0 R 265 0 R 265 0 R 265 0 R 265 0 R 265 0 R 265 0 R 268 0 R 266 0 R 266 0 R 266 0 R 266 0 R 266 0 R 268 0 R 267 0 R 268 0 R 269 0 R 273 0 R 270 0 R 270 0 R 270 0 R 273 0 R 271 0 R 271 0 R 271 0 R 271 0 R 271 0 R 273 0 R 272 0 R 272 0 R 272 0 R 272 0 R 272 0 R 273 0 R 273 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 274 0 R 276 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 275 0 R 276 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 277 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 278 0 R 279 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 280 0 R 281 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 282 0 R 284 0 R 283 0 R 283 0 R 283 0 R 283 0 R 283 0 R 284 0 R 285 0 R 285 0 R 285 0 R 285 0 R 285 0 R 285 0 R 285 0 R 285 0 R 285 0 R 285 0 R 285 0 R 285 0 R 287 0 R 286 0 R] endobj 24 0 obj -[336 0 R 337 0 R 337 0 R 337 0 R 337 0 R 337 0 R 338 0 R 339 0 R 339 0 R 339 0 R 339 0 R 339 0 R 340 0 R 341 0 R 341 0 R 341 0 R 341 0 R 341 0 R 342 0 R 343 0 R 343 0 R 343 0 R 343 0 R 343 0 R 343 0 R 344 0 R 345 0 R 345 0 R 345 0 R 345 0 R 345 0 R 345 0 R 345 0 R 345 0 R 345 0 R 345 0 R 345 0 R 346 0 R 347 0 R 347 0 R 347 0 R 347 0 R 347 0 R 347 0 R 347 0 R 347 0 R 347 0 R 347 0 R 347 0 R 347 0 R 348 0 R 348 0 R 348 0 R 348 0 R 349 0 R 350 0 R 353 0 R 351 0 R 351 0 R 351 0 R 351 0 R 351 0 R 351 0 R 353 0 R 352 0 R 352 0 R 352 0 R 352 0 R 352 0 R 352 0 R 352 0 R 352 0 R 352 0 R 352 0 R 352 0 R 352 0 R 352 0 R 352 0 R 353 0 R 355 0 R 354 0 R 354 0 R 354 0 R 354 0 R 354 0 R 354 0 R 354 0 R 354 0 R 354 0 R 354 0 R 355 0 R 356 0 R 356 0 R 356 0 R 356 0 R 356 0 R 356 0 R 356 0 R 356 0 R 357 0 R 361 0 R 358 0 R 358 0 R 358 0 R 358 0 R 361 0 R 359 0 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Y0yۋ1^hV9ok~y> stream x endstream endobj -472 0 obj +561 0 obj <> stream xmMo0K!!A RP`-9WZDw<m?]Ksi;ftsg3ƶF=j(Q^a1ݶZV(e' !M105A+Q{/2 (2vZ֦ Yr@أҥLpybR (E V 䒣MNOjXH<$:O0C܏֞1 <_!O NSP|}\, g#PPHl'uْsWlYŜGչh/VU5[E=ʤUD=mY=!=ə6j"N%geGZEԐUQ厈+D:*$ -/9>F%aJmǬ!*>q9{ = endstream endobj -473 0 obj +562 0 obj <> stream xV{TWOdx6@Fg}ְu%$!$$$!/BpE#AlqUG[ը ݺ۞}h;aOj=sνY,6,SZ(*$-eǦHs^Qz,l X~ү(_sXX,-c~"tfs'd)2eIwd*zR[ U-;{ظV/ߜ+]~(RjyB*WQP 5f +OkXR2z7-po/[ZrѣHbXK-,*@۪0&d- Kdcgz""st?Aͼ 7S-#ףl3aM'Mkei.=gLg188Wjwh`clD\iL2aE0T fp𒬕 h4+~т{<6 qYHGq7YL&ռ˳4JKӞhWPUt84K rxD&Q;6sH!)%%2JΏ2N (m˾qjk[ +MIY~:x칋ViDhm3-#e, 3=zz(_LC7]~<g.2\abo3uf_ܸaWoIѹ.fӜ\snɛq:a v))MgOE+jmee/'} @@ -1578,19 +1849,19 @@ u v `Rr sKS߆+ @#2m`̓8|ǰ\z{)0M6$>|[^ :}\Pb {w]B N@qc+AgKt z\f &:i#~WWQr2,6E5V[1/ڇnZtmZrz:OAB3Hn.` ­Sn\a K5!E$ Zo?jfX&%\Ja1e)ܸ 5@Q`N[;Eˬ> stream x{ endstream endobj -475 0 obj +564 0 obj <> stream xmQMk0 WhC{ⴰA)-] ~ДJfhlc;a'i6Oz{ӱZ } -E tyߡ{Dbʺ5Cy-Rk/pGyV!h@;;BY+a6 zR߀ hj )C\w#ɨj^F*aG%].AHGo&W7+Ua5DoF&@rV:oo0 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GiB՚HxKFiٕ17;nԻfu۰%`ұ:#5!VsMzWPUHMj.)6j#"݄Zj"yM7uJ]sBcHaɥN"7Ucj9:ʕ2,8WU ;:Ni9%j6F)eYgq]ǴEyfc5F!ӲX;z6"ɑi," uT0q1e0``0Q![ADrI1;u7~ti#5'(JPP endstream endobj -479 0 obj +568 0 obj <> stream x՗n1X#AM.[@0p$EX%x{ԳD3.n_UӃ@w>x8|; ASbHΔ;v9w&@02=!`оuDDGliݦ'yU7Z{92y4<<:M7*JfE'a8y8ER3!ɶ0kW1'.#S="&٨h7^SUyjYsVԨȡ: @@ -1683,7 +1954,7 @@ Mb z i} VKo#Yp?(: R۸[%LNDRsE_\6 ^LJ]Ɯ{K亣[L~: hcB&o''g`U8|%092R/[uUg}Z۪8C*wp\%&qJJh[·RN'y4pk0tnR;D(6{ͬUrZ k{!KR2[UjUrLFrbJ9P`.]Z_njZT2:C!es݁nI[ڋx endstream endobj -480 0 obj +569 0 obj <> stream x}]dql14+1'W --I9 Wra{Gꮼٵ )ҽ}O7Hx>Oӿ|?': O?SCO|OxBQ [,':'< '<7DыzxxRC@9'5\'5q< `j=G ≝/=>g8|?~鋿|~ߜ}ӯ[oog_}_Nx=ii&-/ 틟~8w?Oۇ?<˻iܶ_ >~wܟ~w_&gwg</vA>pz`#Q{4NyV\ Ob_?ŧ{߫'?|wnx_] һ/~!Y;tvk ?_~??ُՋww|qk;b> stream x}]Gn޽~Ep=kgj77$/v aɶ,1i5sd9g4b|~O??/?t>{w=x#pl7|ۏ~}5~7?Dw_|?R*R͠l ٮP ' @@ -1752,7 +2023,7 @@ U Uo7im T.m&^*oCk\KQ%s)͟AY4mTߏ֡p²ϫ+PthЅk(I3N K^h^bqpkw(KdwEY|ꕭgKdYpʦxjO~*g.2>C sbc(.$^9Yw϶MIh?NwTe2)צ":ԧ_ChQ /1YCnZT xѢ^^] endstream endobj -482 0 obj +571 0 obj <> stream 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Пусть даны функторы $phi: cal(J) -> cal(I)$, $alpha: cal(I) -> cal(C)$, $beta: cal(I)^"op" -> cal(C)$. Определите естественные морфизмы $colim(alpha compose phi) -> colim(alpha)$ и $lim(beta) -> lim(beta compose phi^"op")$ в предположении, что все пределы существуют. (Это будет на след. лекции, но попробуйте догадаться самостоятельно). + б) Определим предпучок $f^+ cal(G)$ на $X$ как $f^+ cal(G)(U) = colim_(f(U) subset W) cal(G)(W)$, где копредел берётся по диаграмме, состоящей из множеств $cal(G)(W)$, стрелки между которыми --- отображения ограничения. Определите отображение ограничения для $f^+ cal(G)$ (используйте пункт б')). Этот предпучок называется *обратным образом предпучка* $cal(G)$. +] + +#addinfobox[ + Пояснение: для любого $U subset X$ определим полную poset-подкатегорию $C(U)$ в $Open(Y)^"op"$, состоящую из таких открытых $W subset Y$, что $f(U) subset W$. Тогда имеем функтор $alpha(U, cal(G)): C(U) -> Set$, который получается из функтора $cal(G): Open(Y)^"op" -> Set$ ограничением его на $C(U)$. Тогда $f^+ cal(G)(U)$ --- это копредел по $alpha(U, cal(G))$ для открытого $U subset X$. ] == Решение -=== Для копределов +Будем обозначать $alpha^U_cal(G) := alpha(U, cal(G))$. -Обозначим $iota: alpha ==> colim alpha$, $tau: (alpha compose phi) ==> colim (alpha compose phi)$ --- коконусы. +Хотим привести это всё к виду $colim(alpha compose phi) -> colim alpha$ -Хотим: коконус $psi: (alpha compose phi) ==> colim alpha$. -Построим его с помощью переиндексации -$ psi_j := iota_(phi(j)) $ -Очевидно, это коконус. +Функтор вложения $iota_U: C(U) arrow.hook Open(Y)^op$ просто оставляет объекты и морфизмы на месте. Тогда $alpha^U_cal(G) = cal(G) compose iota_U$. В таком случае ограничения --- это отображения +$ colim (cal(G) compose iota_U) -> colim (cal(G) compose iota_V), space.quad V subset.eq U $ -По универсальному свойству, $forall X in cal(C)$ и коконуса $mu: (alpha compose phi) ==> X$ существует единственное $theta: colim(alpha compose phi) -> X$ т.ч -$ theta compose tau_(j) = mu_(j) $ +Существует вложение категорий $phi^U_V: C(U) arrow.hook C(V)$. +$ op("Ob")(C(U)) = {W in tau_Y | f(U) subset.eq W} $ +$ op("Ob")(C(V)) = {Z in tau_Y | f(V) subset.eq Z} $ +Если $f(V) subset.eq f(U)$, а $f(U) subset.eq Z$ для $Z in op("Ob")(C(U))$, то, очевидно, $f(V) subset.eq Z$. Тогда категории вложены. -Пололжим $X = colim alpha, mu = psi$. -#cdiagram({ - node((-1, -1), [$alpha(phi(j))$]) - node((1, 1), [$op("colim") (alpha compose phi)$]) - node((3, -1), [$alpha (phi(j'))$]) - node((1, 3), [$op("colim") alpha$]) - edge((-1, -1), (3, -1), [$alpha(phi(f))$], label-side: left, "->") - edge((-1, -1), (1, 1), [$tau_j$], label-side: right, "->") - edge((3, -1), (1, 1), [$tau_j'$], label-side: left, "->") - edge((-1, -1), (1, 3), [$psi_j$], label-side: left, "->", bend: -30deg) - edge((3, -1), (1, 3), [$psi_j'$], label-side: left, "->", bend: 30deg) - edge((1, 1), (1, 3), [$theta$], label-side: left, "-->") -}) +Применим б'), подставляя +- $cal(J) = C(U)$ +- $cal(I) = C(V)$ +- $cal(C) = Set$ +- $phi = phi^U_V$ +- $alpha = alpha^V_cal(G)$ + +Тогда существует единственное +$ colim (alpha^V_cal(G) compose phi^U_V) ->^theta colim(alpha^V_cal(G)) $ +Это равно +$ colim (alpha^U_cal(G)) ->^theta colim(alpha^V_cal(G)) $ #answerbox[ #align(center)[ - Определили $theta: colim (alpha compose phi) -> colim alpha$ - ] -] - -=== Для пределов - -Имеем пределы с их каноническими конусами: -- $pi: lim beta ==> beta$ для функтора $beta: cal(I)^"op" -> cal(C)$, -- $q: lim (beta compose phi^"op") ==> (beta compose phi^"op")$ для функтора $beta compose phi^"op": cal(J)^"op" -> cal(C)$. - -Построим конус $p: lim beta ==> (beta compose phi^op)$ с помощью переиндексации: -$ p_j := pi_phi(j) $ - -Тогда по универсальному свойству предела $lim(beta compose phi^"op")$ существует единственный морфизм $eta: lim beta -> lim (beta compose phi^"op")$, делающий диаграмму коммутативной: - -#cdiagram({ - node((0, 4), [$beta(phi(j))$]) - node((4, 4), [$beta(phi(j'))$]) - node((2, 2), [$lim (beta compose phi^"op")$]) - node((2, 0), [$lim beta$]) - edge((4, 4), (0, 4), [$beta(phi(f))$], label-side: left, "->") - edge((2, 2), (0, 4), [$q_j$], label-side: right, "->") - edge((2, 2), (4, 4), [$q_(j')$], label-side: left, "->") - edge((2, 0), (2, 2), [$eta$], label-side: right, "-->") - edge((2, 0), (0, 4), [$p_j$], label-side: right, "->", bend: -30deg) - edge((2, 0), (4, 4), [$p_j'$], label-side: left, "->", bend: 30deg) -}) - -#answerbox[ - #align(center)[ - Определили $eta: lim beta -> lim (beta compose phi^op)$ + Ограничение определяется как + $ theta: f^+ cal(G)(U) -> f^+ cal(G)(V) $ ] ] diff --git a/problems/problem12bprime.typ b/problems/problem12bprime.typ new file mode 100644 index 0000000..6dda961 --- /dev/null +++ b/problems/problem12bprime.typ @@ -0,0 +1,71 @@ +#import "../utils/boxes.typ": * +#import "../utils/macros.typ": * +#import "@preview/fletcher:0.5.8" as fletcher: diagram, node, edge + +#problembox[ + б') Пусть даны категории $cal(I), cal(J), cal(C)$. Пусть даны функторы $phi: cal(J) -> cal(I)$, $alpha: cal(I) -> cal(C)$, $beta: cal(I)^"op" -> cal(C)$. Определите естественные морфизмы $colim(alpha compose phi) -> colim(alpha)$ и $lim(beta) -> lim(beta compose phi^"op")$ в предположении, что все пределы существуют. (Это будет на след. лекции, но попробуйте догадаться самостоятельно). +] + +== Решение + +=== Для копределов + +Обозначим $iota: alpha ==> colim alpha$, $tau: (alpha compose phi) ==> colim (alpha compose phi)$ --- коконусы. + +Хотим: коконус $psi: (alpha compose phi) ==> colim alpha$. +Построим его с помощью переиндексации +$ psi_j := iota_(phi(j)) $ +Очевидно, это коконус. + +По универсальному свойству, $forall X in cal(C)$ и коконуса $mu: (alpha compose phi) ==> X$ существует единственное $theta: colim(alpha compose phi) -> X$ т.ч +$ theta compose tau_(j) = mu_(j) $ + +Пололжим $X = colim alpha, mu = psi$. +#cdiagram({ + node((-1, -1), [$alpha(phi(j))$]) + node((1, 1), [$op("colim") (alpha compose phi)$]) + node((3, -1), [$alpha (phi(j'))$]) + node((1, 3), [$op("colim") alpha$]) + edge((-1, -1), (3, -1), [$alpha(phi(f))$], label-side: left, "->") + edge((-1, -1), (1, 1), [$tau_j$], label-side: right, "->") + edge((3, -1), (1, 1), [$tau_j'$], label-side: left, "->") + edge((-1, -1), (1, 3), [$psi_j$], label-side: left, "->", bend: -30deg) + edge((3, -1), (1, 3), [$psi_j'$], label-side: left, "->", bend: 30deg) + edge((1, 1), (1, 3), [$theta$], label-side: left, "-->") +}) + +#answerbox[ + #align(center)[ + Определили $theta: colim (alpha compose phi) -> colim alpha$ + ] +] + +=== Для пределов + +Имеем пределы с их каноническими конусами: +- $pi: lim beta ==> beta$ для функтора $beta: cal(I)^"op" -> cal(C)$, +- $q: lim (beta compose phi^"op") ==> (beta compose phi^"op")$ для функтора $beta compose phi^"op": cal(J)^"op" -> cal(C)$. + +Построим конус $p: lim beta ==> (beta compose phi^op)$ с помощью переиндексации: +$ p_j := pi_phi(j) $ + +Тогда по универсальному свойству предела $lim(beta compose phi^"op")$ существует единственный морфизм $eta: lim beta -> lim (beta compose phi^"op")$, делающий диаграмму коммутативной: + +#cdiagram({ + node((0, 4), [$beta(phi(j))$]) + node((4, 4), [$beta(phi(j'))$]) + node((2, 2), [$lim (beta compose phi^"op")$]) + node((2, 0), [$lim beta$]) + edge((4, 4), (0, 4), [$beta(phi(f))$], label-side: left, "->") + edge((2, 2), (0, 4), [$q_j$], label-side: right, "->") + edge((2, 2), (4, 4), [$q_(j')$], label-side: left, "->") + edge((2, 0), (2, 2), [$eta$], label-side: right, "-->") + edge((2, 0), (0, 4), [$p_j$], label-side: right, "->", bend: -30deg) + edge((2, 0), (4, 4), [$p_j'$], label-side: left, "->", bend: 30deg) +}) + +#answerbox[ + #align(center)[ + Определили $eta: lim beta -> lim (beta compose phi^op)$ + ] +]