c Max flow problem for tiling p min 180 531 c source node n 0 193 c sink node n 179 -193 c source to target arcs a 0 1 1 1 0 a 0 2 1 1 0 a 0 3 1 1 0 a 0 4 1 1 0 a 0 5 1 1 0 a 0 6 1 1 0 a 0 7 1 1 0 a 0 8 1 1 0 a 0 9 1 1 0 a 0 10 1 1 0 a 0 11 1 1 0 a 0 12 1 1 0 a 0 13 1 1 0 a 0 14 1 1 0 a 0 15 1 1 0 a 0 16 1 1 0 a 0 17 1 1 0 a 0 18 1 1 0 a 0 19 1 1 0 a 0 20 1 1 0 a 0 21 1 1 0 a 0 22 1 1 0 a 0 23 1 1 0 a 0 24 1 1 0 a 0 25 1 1 0 a 0 26 1 1 0 a 0 27 1 1 0 a 0 28 1 2 0 a 0 29 1 1 0 a 0 30 1 1 0 a 0 31 1 1 0 a 0 32 1 1 0 a 0 33 1 1 0 a 0 34 1 1 0 a 0 35 2 3 0 a 0 36 1 1 0 a 0 37 1 1 0 a 0 38 1 1 0 a 0 39 1 1 0 a 0 40 1 1 0 a 0 41 1 1 0 a 0 42 1 1 0 a 0 43 1 1 0 a 0 44 1 2 0 a 0 45 1 1 0 a 0 46 1 1 0 a 0 47 1 1 0 a 0 48 1 1 0 a 0 49 1 1 0 a 0 50 1 1 0 a 0 51 2 3 0 a 0 52 1 1 0 a 0 53 1 1 0 a 0 54 1 1 0 a 0 55 1 2 0 a 0 56 1 1 0 a 0 57 1 1 0 a 0 58 1 1 0 a 0 59 1 1 0 a 0 60 1 1 0 a 0 61 1 1 0 a 0 62 1 1 0 a 0 63 1 1 0 a 0 64 1 1 0 a 0 65 1 1 0 a 0 66 1 1 0 a 0 67 1 1 0 a 0 68 1 2 0 a 0 69 1 1 0 a 0 70 1 1 0 a 0 71 1 2 0 a 0 72 1 1 0 a 0 73 1 1 0 a 0 74 1 1 0 a 0 75 1 1 0 a 0 76 1 1 0 a 0 77 1 1 0 a 0 78 1 1 0 a 0 79 1 1 0 a 0 80 1 1 0 a 0 81 1 1 0 a 0 82 1 1 0 a 0 83 1 2 0 a 0 84 1 1 0 a 0 85 1 2 0 a 0 86 1 1 0 a 0 87 1 1 0 a 0 88 1 1 0 a 0 89 1 1 0 a 0 90 1 1 0 a 0 91 1 1 0 a 0 92 1 1 0 a 0 93 1 1 0 a 0 94 1 2 0 a 0 95 1 1 0 a 0 96 1 1 0 a 0 97 1 1 0 a 0 98 1 1 0 a 0 99 1 1 0 a 0 100 1 1 0 a 0 101 1 1 0 a 0 102 1 1 0 a 0 103 1 2 0 a 0 104 1 2 0 a 0 105 1 1 0 a 0 106 1 1 0 a 0 107 1 1 0 a 0 108 1 1 0 a 0 109 1 1 0 a 0 110 1 1 0 a 0 111 1 1 0 a 0 112 1 1 0 a 0 113 1 1 0 a 0 114 1 1 0 a 0 115 1 2 0 a 0 116 1 1 0 a 0 117 1 1 0 a 0 118 1 2 0 a 0 119 1 1 0 a 0 120 1 1 0 a 0 121 1 1 0 a 0 122 1 1 0 a 0 123 1 1 0 a 0 124 1 1 0 a 0 125 1 1 0 a 0 126 1 1 0 a 0 127 1 1 0 a 0 128 1 1 0 a 0 129 1 1 0 a 0 130 1 1 0 a 0 131 1 1 0 a 0 132 1 1 0 a 0 133 1 1 0 a 0 134 1 1 0 a 0 135 1 1 0 a 0 136 1 1 0 a 0 137 1 1 0 a 0 138 1 1 0 a 0 139 1 1 0 a 0 140 1 1 0 a 0 141 1 1 0 a 0 142 1 1 0 a 0 143 1 1 0 a 0 144 1 1 0 a 0 145 1 1 0 a 0 146 1 1 0 a 0 147 1 1 0 a 0 148 1 1 0 a 0 149 1 1 0 a 0 150 1 2 0 a 0 151 1 1 0 a 0 152 1 1 0 a 0 153 1 1 0 a 0 154 1 1 0 a 0 155 1 1 0 a 0 156 1 1 0 a 0 157 1 1 0 a 0 158 1 1 0 a 0 159 1 1 0 a 0 160 1 1 0 a 0 161 1 1 0 a 0 162 1 1 0 a 0 163 1 1 0 a 0 164 1 1 0 a 0 165 1 1 0 a 0 166 1 1 0 a 0 167 1 1 0 a 0 168 1 1 0 a 0 169 1 1 0 a 0 170 1 1 0 a 0 171 1 1 0 a 0 172 1 1 0 a 0 173 1 1 0 a 0 174 1 1 0 a 0 175 1 1 0 a 0 176 1 1 0 c target to tile arcs a 1 177 0 1 0 a 1 178 0 1 0 a 2 177 0 1 0 a 2 178 0 1 0 a 3 177 0 1 0 a 3 178 0 1 0 a 4 177 0 1 0 a 4 178 0 1 0 a 5 177 0 1 0 a 5 178 0 1 0 a 6 177 0 1 0 a 6 178 0 1 0 a 7 177 0 1 0 a 7 178 0 1 0 a 8 177 0 1 0 a 8 178 0 1 0 a 9 177 0 1 0 a 9 178 0 1 0 a 10 177 0 1 0 a 10 178 0 1 0 a 11 177 0 1 0 a 11 178 0 1 0 a 12 177 0 1 0 a 12 178 0 1 0 a 13 177 0 1 0 a 13 178 0 1 0 a 14 177 0 1 0 a 14 178 0 1 0 a 15 177 0 1 0 a 15 178 0 1 0 a 16 177 0 1 0 a 16 178 0 1 0 a 17 177 0 1 0 a 17 178 0 1 0 a 18 177 0 1 0 a 18 178 0 1 0 a 19 177 0 1 0 a 19 178 0 1 0 a 20 177 0 1 0 a 20 178 0 1 0 a 21 177 0 1 0 a 21 178 0 1 0 a 22 177 0 1 0 a 22 178 0 1 0 a 23 177 0 1 0 a 23 178 0 1 0 a 24 177 0 1 0 a 24 178 0 1 0 a 25 177 0 1 0 a 25 178 0 1 0 a 26 177 0 1 0 a 26 178 0 1 0 a 27 177 0 1 0 a 27 178 0 1 0 a 28 177 0 1 0 a 28 178 0 1 0 a 29 177 0 1 0 a 29 178 0 1 0 a 30 177 0 1 0 a 30 178 0 1 0 a 31 177 0 1 0 a 31 178 0 1 0 a 32 177 0 1 0 a 32 178 0 1 0 a 33 177 0 1 0 a 33 178 0 1 0 a 34 177 0 1 0 a 34 178 0 1 0 a 35 177 0 2 0 a 35 178 0 2 0 a 36 177 0 1 0 a 36 178 0 1 0 a 37 177 0 1 0 a 37 178 0 1 0 a 38 177 0 1 0 a 38 178 0 1 0 a 39 177 0 1 0 a 39 178 0 1 0 a 40 177 0 1 0 a 40 178 0 1 0 a 41 177 0 1 0 a 41 178 0 1 0 a 42 177 0 1 0 a 42 178 0 1 0 a 43 177 0 1 0 a 43 178 0 1 0 a 44 177 0 1 0 a 44 178 0 1 0 a 45 177 0 1 0 a 45 178 0 1 0 a 46 177 0 1 0 a 46 178 0 1 0 a 47 177 0 1 0 a 47 178 0 1 0 a 48 177 0 1 0 a 48 178 0 1 0 a 49 177 0 1 0 a 49 178 0 1 0 a 50 177 0 1 0 a 50 178 0 1 0 a 51 177 0 2 0 a 51 178 0 2 0 a 52 177 0 1 0 a 52 178 0 1 0 a 53 177 0 1 0 a 53 178 0 1 0 a 54 177 0 1 0 a 54 178 0 1 0 a 55 177 0 1 0 a 55 178 0 1 0 a 56 177 0 1 0 a 56 178 0 1 0 a 57 177 0 1 0 a 57 178 0 1 0 a 58 177 0 1 0 a 58 178 0 1 0 a 59 177 0 1 0 a 59 178 0 1 0 a 60 177 0 1 0 a 60 178 0 1 0 a 61 177 0 1 0 a 61 178 0 1 0 a 62 177 0 1 0 a 62 178 0 1 0 a 63 177 0 1 0 a 63 178 0 1 0 a 64 177 0 1 0 a 64 178 0 1 0 a 65 177 0 1 0 a 65 178 0 1 0 a 66 177 0 1 0 a 66 178 0 1 0 a 67 177 0 1 0 a 67 178 0 1 0 a 68 177 0 1 0 a 68 178 0 1 0 a 69 177 0 1 0 a 69 178 0 1 0 a 70 177 0 1 0 a 70 178 0 1 0 a 71 177 0 1 0 a 71 178 0 1 0 a 72 177 0 1 0 a 72 178 0 1 0 a 73 177 0 1 0 a 73 178 0 1 0 a 74 177 0 1 0 a 74 178 0 1 0 a 75 177 0 1 0 a 75 178 0 1 0 a 76 177 0 1 0 a 76 178 0 1 0 a 77 177 0 1 0 a 77 178 0 1 0 a 78 177 0 1 0 a 78 178 0 1 0 a 79 177 0 1 0 a 79 178 0 1 0 a 80 177 0 1 0 a 80 178 0 1 0 a 81 177 0 1 0 a 81 178 0 1 0 a 82 177 0 1 0 a 82 178 0 1 0 a 83 177 0 1 0 a 83 178 0 1 0 a 84 177 0 1 0 a 84 178 0 1 0 a 85 177 0 1 0 a 85 178 0 1 0 a 86 177 0 1 0 a 86 178 0 1 0 a 87 177 0 1 0 a 87 178 0 1 0 a 88 177 0 1 0 a 88 178 0 1 0 a 89 177 0 1 0 a 89 178 0 1 0 a 90 177 0 1 0 a 90 178 0 1 0 a 91 177 0 1 0 a 91 178 0 1 0 a 92 177 0 1 0 a 92 178 0 1 0 a 93 177 0 1 0 a 93 178 0 1 0 a 94 177 0 1 0 a 94 178 0 1 0 a 95 177 0 1 0 a 95 178 0 1 0 a 96 177 0 1 0 a 96 178 0 1 0 a 97 177 0 1 0 a 97 178 0 1 0 a 98 177 0 1 0 a 98 178 0 1 0 a 99 177 0 1 0 a 99 178 0 1 0 a 100 177 0 1 0 a 100 178 0 1 0 a 101 177 0 1 0 a 101 178 0 1 0 a 102 177 0 1 0 a 102 178 0 1 0 a 103 177 0 1 0 a 103 178 0 1 0 a 104 177 0 1 0 a 104 178 0 1 0 a 105 177 0 1 0 a 105 178 0 1 0 a 106 177 0 1 0 a 106 178 0 1 0 a 107 177 0 1 0 a 107 178 0 1 0 a 108 177 0 1 0 a 108 178 0 1 0 a 109 177 0 1 0 a 109 178 0 1 0 a 110 177 0 1 0 a 110 178 0 1 0 a 111 177 0 1 0 a 111 178 0 1 0 a 112 177 0 1 0 a 112 178 0 1 0 a 113 177 0 1 0 a 113 178 0 1 0 a 114 177 0 1 0 a 114 178 0 1 0 a 115 177 0 1 0 a 115 178 0 1 0 a 116 177 0 1 0 a 116 178 0 1 0 a 117 177 0 1 0 a 117 178 0 1 0 a 118 177 0 1 0 a 118 178 0 1 0 a 119 177 0 1 0 a 119 178 0 1 0 a 120 177 0 1 0 a 120 178 0 1 0 a 121 177 0 1 0 a 121 178 0 1 0 a 122 177 0 1 0 a 122 178 0 1 0 a 123 177 0 1 0 a 123 178 0 1 0 a 124 177 0 1 0 a 124 178 0 1 0 a 125 177 0 1 0 a 125 178 0 1 0 a 126 177 0 1 0 a 126 178 0 1 0 a 127 177 0 1 0 a 127 178 0 1 0 a 128 177 0 1 0 a 128 178 0 1 0 a 129 177 0 1 0 a 129 178 0 1 0 a 130 177 0 1 0 a 130 178 0 1 0 a 131 177 0 1 0 a 131 178 0 1 0 a 132 177 0 1 0 a 132 178 0 1 0 a 133 177 0 1 0 a 133 178 0 1 0 a 134 177 0 1 0 a 134 178 0 1 0 a 135 177 0 1 0 a 135 178 0 1 0 a 136 177 0 1 0 a 136 178 0 1 0 a 137 177 0 1 0 a 137 178 0 1 0 a 138 177 0 1 0 a 138 178 0 1 0 a 139 177 0 1 0 a 139 178 0 1 0 a 140 177 0 1 0 a 140 178 0 1 0 a 141 177 0 1 0 a 141 178 0 1 0 a 142 177 0 1 0 a 142 178 0 1 0 a 143 177 0 1 0 a 143 178 0 1 0 a 144 177 0 1 0 a 144 178 0 1 0 a 145 177 0 1 0 a 145 178 0 1 0 a 146 177 0 1 0 a 146 178 0 1 0 a 147 177 0 1 0 a 147 178 0 1 0 a 148 177 0 1 0 a 148 178 0 1 0 a 149 177 0 1 0 a 149 178 0 1 0 a 150 177 0 1 0 a 150 178 0 1 0 a 151 177 0 1 0 a 151 178 0 1 0 a 152 177 0 1 0 a 152 178 0 1 0 a 153 177 0 1 0 a 153 178 0 1 0 a 154 177 0 1 0 a 154 178 0 1 0 a 155 177 0 1 0 a 155 178 0 1 0 a 156 177 0 1 0 a 156 178 0 1 0 a 157 177 0 1 0 a 157 178 0 1 0 a 158 177 0 1 0 a 158 178 0 1 0 a 159 177 0 1 0 a 159 178 0 1 0 a 160 177 0 1 0 a 160 178 0 1 0 a 161 177 0 1 0 a 161 178 0 1 0 a 162 177 0 1 0 a 162 178 0 1 0 a 163 177 0 1 0 a 163 178 0 1 0 a 164 177 0 1 0 a 164 178 0 1 0 a 165 177 0 1 0 a 165 178 0 1 0 a 166 177 0 1 0 a 166 178 0 1 0 a 167 177 0 1 0 a 167 178 0 1 0 a 168 177 0 1 0 a 168 178 0 1 0 a 169 177 0 1 0 a 169 178 0 1 0 a 170 177 0 1 0 a 170 178 0 1 0 a 171 177 0 1 0 a 171 178 0 1 0 a 172 177 0 1 0 a 172 178 0 1 0 a 173 177 0 1 0 a 173 178 0 1 0 a 174 177 0 1 0 a 174 178 0 1 0 a 175 177 0 1 0 a 175 178 0 1 0 a 176 177 0 1 0 a 176 178 0 1 0 c tile to sink arcs a 177 179 0 592 0 a 178 179 0 592 0 c overflow arc a 0 179 0 193 1000 c end of flow problem