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 |    N |   O |   P |    Q |   R |    S |    T |    U |    V |    W |
|----:|:---------------------|:-----------|----:|-----:|----:|----:|----:|----:|----:|----:|----:|----:|-----:|----:|----:|-----:|----:|-----:|-----:|-----:|-----:|-----:|
|   1 | Alirajpur            | BOB        |  24 |  615 |   1 |  17 |   0 |  26 |   0 |  26 |  12 | 304 |    4 | 117 |   7 |  128 |  47 | 1186 |  151 |  375 |   19 |  545 |
|   2 | Anuppur              | CBI        |  22 |  660 |   8 | 201 |   1 |   2 |   0 |   2 |  14 | 386 |   45 | 122 |   5 |  172 |  28 |  723 |   71 |  171 |    5 |  247 |
|   3 | Ashok Nagar          | SBI        |  30 |  750 |   2 |  57 |  83 |  60 |   0 |  60 |  27 | 665 |   93 | 184 | 201 |  478 |  70 | 1673 |  355 |  358 |  296 | 1009 |
|   4 | Balaghat             | CBI        |  14 |  400 |   2 |  53 |   0 |   0 |   0 |   0 |  26 | 636 |   18 | 306 |  30 |  354 |  47 | 1290 |   41 |  837 |   30 |  908 |
|   5 | Barwani              | BOI        |  25 |  750 |   8 | 278 |   0 |   2 |   0 |   2 |  26 | 636 |   18 | 302 |  30 |  350 |  47 | 1290 |   41 |  833 |   30 |  904 |
|   6 | Betul                | CBI        |  16 |  400 |   1 |  25 |  30 |   4 |   0 |   4 |  12 | 232 |   46 |  16 |   0 |   62 |  30 |  633 |  171 |   94 |    6 |  271 |
|   7 | Bhind                | CBI        |  25 |  750 |   2 |  39 |  37 |  91 |  59 | 150 |  21 | 530 |   97 | 289 |  85 |  471 |  34 |  849 |  105 |  330 |   86 |  521 |
|   8 | Bhopal (BOI)         | BOI        |  25 |  750 |   3 |  58 | 241 |   0 |   0 |   0 |  20 | 432 |  468 | 150 |   2 |  620 |  97 | 2292 | 1212 |  600 |  251 | 2063 |
|   9 | Bhopal (RUDSETI)     | RUDSETI    |  25 |  750 |   2 |  61 |  23 |  22 |   7 |  29 |  26 | 781 |   62 | 238 | 132 |  432 | 250 | 7869 | 1325 | 3206 | 1005 | 5536 |
|  10 | Burhanpur            | BOI        |  25 |  750 |   6 | 231 |  38 | 185 |   3 | 188 |  20 | 611 |   49 | 281 |  38 |  368 |  50 | 1367 |   91 |  782 |  114 |  987 |
|  11 | Chhatarpur           | SBI        |  28 |  840 |   2 |  82 |   0 |  37 |   1 |  38 |  21 | 651 |   12 | 150 |  12 |  174 | 109 | 2881 |  554 |  852 |   61 | 1467 |
|  12 | Chhindwara           | CBI        |  18 |  540 |   6 | 145 |   0 |   0 |   0 |   0 |  15 | 378 |    0 |   8 |   0 |    8 |  50 | 1391 |  462 |   50 |   20 |  532 |
|  13 | Damoh                | SBI        |  26 |  780 |   9 | 250 |   0 |  27 |  35 |  62 |  27 | 707 |   55 | 180 | 255 |  490 | 124 | 3580 |  390 |  689 |  935 | 2014 |
|  14 | Datia                | PNB        |  30 |  750 |   3 |  81 |   3 | 136 |   2 | 138 |  30 | 756 |    9 | 456 |  29 |  494 | 198 | 5203 | 1207 | 1253 |  495 | 2955 |
|  15 | Dewas                | BOI        |  26 |  780 |   2 |  55 |   0 |   0 |   0 |   0 |  19 | 537 |   99 |  66 |  31 |  196 |  73 | 1930 |  511 |  343 |  154 | 1008 |
|  16 | Dhar                 | BOI        |  20 |  600 |   1 |  24 |   0 |   0 |   0 |   0 |  11 | 354 |    2 | 169 |  16 |  187 |  31 | 1035 |  367 |  329 |   20 |  716 |
|  17 | Dindori              | CBI        |  14 |  400 |   6 | 210 |   0 |   0 |   0 |   0 |  20 | 569 |   31 |  44 |  26 |  101 |  81 | 2725 | 1326 |  130 |   26 | 1482 |
|  18 | Guna                 | SBI        |  30 |  750 |   3 |  91 |   0 |  20 | 149 | 169 |  21 | 623 |    0 | 105 | 275 |  380 |  82 | 2396 |  235 |  441 |  624 | 1300 |
|  19 | Gwalior              | CBI        |  25 |  750 |   2 |  48 |  22 |   0 |  25 |  25 |  18 | 422 |  135 |  47 |  26 |  208 |  82 | 1781 |  810 |  127 |   34 |  971 |
|  20 | Harda                | SBI        |  25 |  750 |   7 | 153 |   0 |   0 |   0 |   0 |  17 | 383 |    0 |  66 |  37 |  103 |  48 | 1288 |   80 |  375 |  177 |  632 |
|  21 | Hoshangabad          | CBI        |  12 |  400 |   3 |  90 | 113 |   1 |   0 |   1 |  19 | 427 |  247 |  19 |   0 |  266 |  78 | 2322 | 1045 |  202 |   17 | 1264 |
|  22 | Indore               | Vijya Bank |  25 |  750 |   2 |  39 |   3 |  26 |   6 |  32 |  19 | 380 |   73 | 252 |  96 |  421 |  76 | 1560 |  265 |  592 |  299 | 1156 |
|  23 | Jabalpur             | CBI        |  20 |  600 |   2 |  64 |  10 |  30 |   0 |  30 |  12 | 350 |  135 | 235 |  48 |  418 |  95 | 2903 | 1679 |  284 |   69 | 2032 |
|  24 | Jhabua               | BOB        |  30 |  800 |   1 |  27 |   0 |   0 |   0 |   0 |  20 | 661 |   11 | 214 |   0 |  225 |  91 | 2845 |  118 | 1162 |    0 | 1280 |
|  25 | Katni                | SBI        |  26 |  760 |   4 | 100 |   0 |  19 |   0 |  19 |  24 | 628 |  196 | 263 |  72 |  531 |  59 | 1569 |  219 |  623 |  128 |  970 |
|  26 | Khandwa (East Nimar) | BOI        |  25 |  750 |   4 | 137 |  19 |  89 |   0 |  89 |  18 | 502 |   48 | 303 |  50 |  401 |  81 | 2066 |  537 |  592 |   59 | 1188 |
|  27 | Khargone             | BOI        |  25 |  750 |   3 | 120 |   0 |   0 |   0 |   0 |  19 | 565 |   62 | 162 |  34 |  258 |  46 | 1291 |  114 |  379 |   70 |  563 |
|  28 | Mandla               | CBI        |  25 |  750 |   4 | 147 |   0 |   0 |   0 |   0 |  14 | 325 |   37 |  40 |  17 |   94 |  37 |  934 |  161 |  277 |   24 |  462 |
|  29 | Mandsaur             | CBI        |  12 |  400 |   3 | 103 |   2 |  85 | 100 | 185 |  20 | 555 |    7 | 104 | 123 |  234 |  58 | 1654 |  592 |  202 |  292 | 1086 |
|  30 | Morena               | CBI        |  25 |  750 |   1 |  23 |  16 |  23 |  23 |  46 |  13 | 395 |   21 | 142 |  47 |  210 |  35 | 1253 |  286 |  446 |   77 |  809 |
|  31 | Narsinghpur          | CBI        |  25 |  750 |   1 |  30 |  40 | 165 |   1 | 166 |  21 | 591 |   42 | 255 |  29 |  326 | 137 | 6333 | 1932 |  701 | 2291 | 4924 |
|  32 | Neemuch              | SBI        |  29 |  870 |   4 |  79 |   0 |   0 |   2 |   2 |  19 | 443 |    0 | 224 | 213 |  437 |  51 | 1208 |    1 |  441 |  416 |  858 |
|  33 | Panna                | SBI        |  25 |  750 |   5 | 142 |   0 | 120 |   0 | 120 |  24 | 624 |    1 | 298 |   0 |  299 |  84 | 2094 |  501 |  677 |  132 | 1310 |
|  34 | Raisen               | CBI        |  24 |  720 |   1 |  28 |   0 |   0 |   0 |   0 |  23 | 660 | 1159 |  30 |   0 | 1189 |  67 | 2191 | 1642 |   30 |    0 | 1672 |
|  35 | Rajgarh              | BOI        |  28 |  750 |   0 |   0 | 159 |  31 |   1 |  32 |  30 | 872 |  698 |  66 |  77 |  841 | 108 | 3377 | 2315 |  230 |  141 | 2686 |
|  36 | Ratlam               | CBI        |  29 |  750 |   3 | 100 |  32 |   0 |   0 |   0 |  24 | 777 |  201 | 414 |   0 |  615 |  76 | 2649 |  588 | 1343 |    0 | 1931 |
|  37 | Rewa                 | UBI        |  30 |  750 |   1 |  18 |  36 |  27 |   0 |  27 |  29 | 799 |  209 | 329 |   8 |  546 |  90 | 2385 |  364 | 1062 |   47 | 1473 |
|  38 | Sagar                | CBI        |  39 | 1170 |   7 | 201 |   0 |  13 |   0 |  13 |  24 | 732 |   13 | 121 |   0 |  134 | 111 | 3516 | 1755 |  643 |    0 | 2398 |
|  39 | Satna                | All. Bank  |  27 |  750 |   3 |  96 |   1 |  32 |  43 |  75 |  25 | 750 |   38 | 488 |  61 |  587 |  92 | 2808 |  392 | 1584 |  166 | 2142 |
|  40 | Sehore               | BOI        |  24 |  750 |   0 |   0 |   0 |   0 |   0 |   0 |   9 | 222 |   22 |  21 |   0 |   43 |  59 | 1964 | 1360 |  208 |   29 | 1597 |
|  41 | Seoni                | CBI        |  14 |  400 |   2 |  57 |   2 |   5 |   0 |   5 |  13 | 358 |   38 |  50 |  12 |  100 |  29 |  820 |   89 |  179 |   47 |  315 |
|  42 | shahdol              | CBI        |  29 |  870 |   0 |   0 |   0 | 146 |   0 | 146 |  30 | 912 |  143 | 260 |   0 |  403 |  87 | 2827 |  714 | 1013 |   99 | 1826 |
|  43 | Shajapur             | BOI        |  32 |  900 |   3 | 100 |   0 |   0 |   0 |   0 |   9 | 222 |   22 |  21 |   0 |   43 |  82 | 2119 |   40 |  670 |   54 |  764 |
|  44 | Sheopur              | SBI        |  25 |  625 |   5 | 147 |   0 |  56 |   0 |  56 |  20 | 549 |    4 | 117 |   0 |  121 |  81 | 2311 |  291 |  925 |    1 | 1217 |
|  45 | Shivpuri             | SBI        |  27 |  750 |   3 |  79 |   9 |  49 |  16 |  65 |  25 | 558 |  129 | 209 |  49 |  387 |  87 | 2146 |  401 |  725 |  187 | 1313 |
|  46 | Sidhi                | UBI        |  22 |  645 |   3 |  84 |  37 | 218 |   0 | 218 |  24 | 724 |   61 | 330 |   0 |  391 |  42 | 1286 |  168 |  478 |   68 |  714 |
|  47 | Singrauli            | UBI        |  24 |  600 |   2 |  32 |  26 |   0 |   0 |   0 |  25 | 593 |   88 | 135 |  75 |  298 |  45 | 1104 |  421 |  172 |   75 |  668 |
|  48 | Tikamgarh            | SBI        |  25 |  750 |   6 | 207 |   0 |  83 |   0 |  83 |  25 | 662 |    4 | 307 | 108 |  419 |  85 | 2220 |   75 |  818 |  195 | 1088 |
|  49 | Ujjain               | BOI        |  25 |  750 |   3 |  60 |   0 |   0 |   0 |   0 |  16 | 333 |   17 |  48 |   0 |   65 |  45 | 1088 |  249 |  261 |    0 |  510 |
|  50 | Umaria               | SBI        |  29 |  800 |   7 | 153 |   0 |   0 |   0 |   0 |  23 | 503 |   48 | 220 |  59 |  327 |  79 | 2063 |  396 |  594 |  241 | 1231 |
|  51 | Vidisha              | SBI        |  26 |  780 |   4 |  95 |   0 |  22 |   0 |  22 |  19 | 402 |   55 | 130 |  32 |  217 |  66 | 1564 |  152 |  541 |  246 |  939 |



label: Q=P+O+N
W=V+U+T
labeled_formulas: Q=P+O+N
W=V+U+T
output: {"Arithmetic-Relationship": ["Q=P+O+N", "W=V+U+T"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_105623___xlsx_4c6067c95c5db456896c32d827970c92d88dce36.xlsx___line_212