Task: Arithmetic-Relationship (source dataset: Auto-Relate)

You are given a table with numerical values in multiple columns. Your task is to analyze the data and identify semantic relationships, expressed in arithmetic relationships, that exist between columns.

These relationships may involve any combination of the following operations: addition (+), subtraction (−), multiplication (*), and division (/). The expressions can involve two or more columns and may be nested (e.g., B = (A + C) / D).

Please only identify arithmetic relationships that hold semantically based on the data, and do not return relationships that are likely spurious, e.g., (A = B * 0), where A is an all 0 column. Please only return minimal atomic relationships, e.g., if A = B + C and D = E + F, then there is no need to return A = B + C + E + F - D.

No explanation, return all the formula(s) in JSON format: {"Arithmetic-Relationship": [<list-of-formulas>]}. If no relationship is found, return {"Arithmetic-Relationship": []}.

Input Table:
| A                    |   B |   C |   D |   E |   F |   G |   H |   I |   J |   K |   L |   M |
|:---------------------|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|
| Arkwright            | 424 |  99 |  84 |  15 | 294 | 199 |  62 |   6 |  27 |   0 |   0 |  31 |
| Busti 1              | 593 | 147 | 137 |  10 | 428 | 356 |  49 |   8 |  15 |   0 |   0 |  18 |
| Busti 2              | 459 | 114 | 110 |   4 | 326 | 269 |  35 |   2 |  20 |   0 |   0 |  19 |
| Busti 4              | 284 |  53 |  48 |   5 | 224 | 195 |  23 |   2 |   4 |   0 |   0 |   7 |
| Busti 5              | 448 |  68 |  65 |   3 | 352 | 295 |  43 |   3 |  11 |   0 |   0 |  28 |
| Carroll 1            | 614 |  84 |  70 |  14 | 487 | 353 |  85 |  13 |  36 |   0 |   0 |  43 |
| Charlotte            | 396 |  64 |  56 |   8 | 323 | 253 |  57 |   4 |   9 |   0 |   0 |   9 |
| Chautauqua 1         | 403 | 113 | 107 |   6 | 275 | 216 |  29 |   6 |  24 |   0 |   0 |  15 |
| Chautauqua 4         |  70 |   5 |   4 |   1 |  64 |  49 |   9 |   1 |   5 |   0 |   0 |   1 |
| Cherry Creek         | 220 |  42 |  37 |   5 | 173 | 134 |  33 |   1 |   5 |   0 |   0 |   5 |
| Clymer               | 270 |  31 |  29 |   2 | 231 | 198 |  25 |   5 |   3 |   0 |   0 |   8 |
| Dunkirk Town 1       | 140 |  30 |  27 |   3 | 108 |  85 |   9 |   2 |  12 |   0 |   0 |   2 |
| Dunkirk Town 2       | 166 |  41 |  38 |   3 | 119 | 101 |   7 |   6 |   5 |   0 |   0 |   6 |
| Dunkirk - Ward 1-1   | 135 |  65 |  60 |   5 |  60 |  46 |   9 |   1 |   4 |   0 |   0 |  10 |
| Dunkirk - Ward 1-2   | 370 | 151 | 135 |  16 | 201 | 163 |  26 |   5 |   7 |   0 |   0 |  18 |
| Dunkirk - Ward 1-3   | 323 | 104 |  94 |  10 | 205 | 161 |  24 |   1 |  19 |   0 |   0 |  14 |
| Dunkirk - Ward 2-1   | 302 | 118 | 112 |   6 | 167 | 126 |  23 |   3 |  15 |   0 |   0 |  17 |
| Dunkirk - Ward 2-3   | 257 |  62 |  57 |   5 | 179 | 143 |  20 |   1 |  15 |   0 |   0 |  16 |
| Dunkirk - Ward 3-2   | 197 |  73 |  67 |   6 | 119 |  92 |  20 |   3 |   4 |   0 |   0 |   5 |
| Dunkirk - Ward 3-3   | 332 |  80 |  71 |   9 | 241 | 191 |  33 |   3 |  14 |   0 |   0 |  11 |
| Dunkirk - Ward 4-1   | 211 | 116 | 110 |   6 |  74 |  55 |  12 |   2 |   5 |   0 |   0 |  21 |
| Dunkirk - Ward 4-3   | 230 |  64 |  57 |   7 | 154 | 120 |  18 |   0 |  16 |   0 |   0 |  12 |
| Ellery 2V            | 101 |  16 |  16 |   0 |  76 |  65 |   6 |   1 |   4 |   0 |   0 |   9 |
| Ellery 3             | 336 |  67 |  65 |   2 | 259 | 219 |  27 |   6 |   7 |   0 |   0 |  10 |
| Ellicott - Ward 1-2  | 181 |  57 |  54 |   3 | 119 |  93 |  15 |   1 |  10 |   0 |   0 |   5 |
| Ellicott - Ward 2-1  | 375 | 102 |  90 |  12 | 263 | 223 |  27 |   4 |   9 |   0 |   0 |  10 |
| Ellicott - Ward 2-2  | 112 |  34 |  31 |   3 |  77 |  66 |   7 |   2 |   2 |   0 |   0 |   1 |
| Ellicott- Ward 2-3   |  43 |  11 |  10 |   1 |  32 |  27 |   5 |   0 |   0 |   0 |   0 |   0 |
| Ellicott - Ward 3-1  | 235 |  66 |  57 |   9 | 158 | 122 |  18 |   5 |  13 |   0 |   0 |  11 |
| Ellicott - Ward 3-2  | 197 |  35 |  31 |   4 | 160 | 131 |  20 |   4 |   5 |   0 |   0 |   2 |
| Ellicott - Ward 4-1  | 148 |  34 |  31 |   3 | 110 |  89 |   9 |   5 |   7 |   0 |   0 |   4 |
| Ellicott - Ward 4-2  |  21 |   4 |   4 |   0 |  16 |  13 |   2 |   1 |   0 |   0 |   0 |   1 |
| Ellicott - Ward 4-3  | 299 |  51 |  49 |   2 | 242 | 210 |  26 |   1 |   5 |   0 |   0 |   6 |
| Ellington            | 532 |  93 |  79 |  14 | 383 | 323 |  36 |   6 |  18 |   0 |   0 |  56 |
| French Creek         | 158 |  20 |  18 |   2 | 135 | 126 |   8 |   1 |   0 |   0 |   0 |   3 |
| Gerry                | 406 |  42 |  35 |   7 | 354 | 291 |  48 |   8 |   7 |   0 |   0 |  10 |
| Hanover 1            | 334 |  66 |  61 |   5 | 265 | 184 |  46 |   7 |  28 |   0 |   0 |   3 |
| Hanover 3            | 389 |  66 |  62 |   4 | 320 | 251 |  43 |   3 |  23 |   0 |   0 |   3 |
| Hanover 4            | 353 |  59 |  58 |   1 | 291 | 227 |  41 |   7 |  16 |   0 |   0 |   3 |
| Harmony 1            | 309 |  72 |  65 |   7 | 226 | 191 |  27 |   2 |   6 |   0 |   0 |  11 |
| Harmony 2            | 116 |  19 |  16 |   3 |  97 |  83 |  12 |   1 |   1 |   0 |   0 |   0 |
| Jamestown - Ward 1-1 | 157 |  65 |  60 |   5 |  84 |  74 |   6 |   1 |   3 |   0 |   0 |   8 |
| Jamestown - Ward 1-2 | 291 | 108 |  98 |  10 | 164 | 133 |  19 |   3 |   9 |   0 |   0 |  19 |
| Jamestown - Ward 1-3 | 370 | 114 | 109 |   5 | 244 | 206 |  20 |   8 |  10 |   0 |   0 |  12 |
| Jamestown - Ward 2-1 | 107 |  50 |  42 |   8 |  52 |  39 |   4 |   5 |   4 |   0 |   0 |   5 |
| Jamestown - Ward 2-2 | 306 | 134 | 128 |   6 | 155 | 121 |  14 |   9 |  11 |   0 |   0 |  17 |
| Jamestown - Ward 2-3 | 515 | 199 | 186 |  13 | 302 | 240 |  34 |  11 |  17 |   0 |   0 |  14 |
| Jamestown - Ward 3-3 | 112 |  39 |  36 |   3 |  68 |  52 |  13 |   1 |   2 |   0 |   0 |   5 |
| Jamestown - Ward 3-4 |  12 |   8 |   8 |   0 |   4 |   3 |   1 |   0 |   0 |   0 |   0 |   0 |
| Jamestown - Ward 4-1 | 435 | 173 | 160 |  13 | 247 | 201 |  34 |   4 |   8 |   0 |   0 |  15 |
| Jamestown - Ward 5-1 | 245 | 100 |  95 |   5 | 133 | 110 |  15 |   2 |   6 |   0 |   0 |  12 |
| Jamestown - Ward 5-3 | 418 | 125 | 122 |   3 | 265 | 216 |  31 |   6 |  12 |   0 |   0 |  28 |
| Jamestown - Ward 6-2 | 173 |  61 |  52 |   9 | 106 |  80 |  16 |   6 |   4 |   0 |   0 |   6 |
| Jamestown - Ward 6-3 | 313 | 101 |  90 |  11 | 198 | 150 |  31 |   3 |  14 |   0 |   0 |  14 |
| Kiantone             | 357 |  82 |  77 |   5 | 269 | 231 |  20 |  10 |   8 |   0 |   0 |   6 |
| Mina                 | 314 |  54 |  50 |   4 | 246 | 215 |  21 |   2 |   8 |   0 |   0 |  14 |
| North Harmony 1      | 280 |  80 |  71 |   9 | 193 | 165 |  17 |   1 |  10 |   0 |   0 |   7 |
| North Harmony 2      | 252 |  54 |  50 |   4 | 193 | 150 |  30 |   5 |   8 |   0 |   0 |   5 |
| Poland 1             | 293 |  59 |  53 |   6 | 223 | 190 |  28 |   0 |   5 |   0 |   0 |  11 |
| Pomfret 1            | 542 | 135 | 119 |  16 | 394 | 316 |  43 |   6 |  29 |   0 |   0 |  13 |
| Pomfret 2            | 371 | 134 | 126 |   8 | 229 | 187 |  22 |   3 |  17 |   0 |   0 |   8 |
| Pomfret 3            | 504 | 130 | 120 |  10 | 365 | 292 |  47 |   5 |  21 |   0 |   0 |   9 |
| Pomfret 4            | 608 | 238 | 217 |  21 | 352 | 270 |  43 |   6 |  33 |   0 |   0 |  18 |
| Pomfret 6            | 152 |  47 |  43 |   4 | 104 |  82 |  10 |   4 |   8 |   0 |   0 |   1 |
| Pomfret 8            | 352 |  88 |  84 |   4 | 259 | 205 |  24 |   2 |  28 |   0 |   0 |   5 |
| Ripley 2             | 351 |  87 |  69 |  18 | 236 | 187 |  35 |   0 |  14 |   0 |   0 |  28 |
| Sheridan 1           | 268 |  50 |  46 |   4 | 215 | 157 |  45 |   3 |  10 |   0 |   0 |   3 |
| Sherman              | 125 |  17 |  16 |   1 | 106 |  88 |  12 |   0 |   6 |   0 |   0 |   2 |
| Sherman V            | 180 |  35 |  32 |   3 | 135 | 107 |  20 |   7 |   1 |   0 |   0 |  10 |
| Stockton 1           | 264 |  41 |  35 |   6 | 218 | 189 |  24 |   0 |   5 |   0 |   0 |   5 |
| Stockton 2           |  29 |   4 |   4 |   0 |  25 |  21 |   4 |   0 |   0 |   0 |   0 |   0 |
| Stockton 2V          | 203 |  49 |  43 |   6 | 150 | 124 |  17 |   0 |   9 |   0 |   0 |   4 |
| Villenova            | 310 |  76 |  71 |   5 | 220 | 143 |  24 |  45 |   8 |   0 |   0 |  14 |
| Westfield 2          | 318 |  92 |  84 |   8 | 219 | 173 |  33 |   0 |  13 |   0 |   0 |   7 |
| Westfield 3          | 392 | 107 |  99 |   8 | 274 | 219 |  34 |   7 |  14 |   0 |   0 |  11 |



labeled_formulas: K=(C-D)-E
L=(C-D)-E
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_19020___xlsx_dbdbffa7e99454166aef45fd2836e85cdbeba4dc.xlsx___line_668