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 |
|-------:|----:|:-------|--------:|:------------------------------------------------------------|:-------------------------------|:-------------------------------|:------------------|:----|------:|------:|------:|----:|---------:|------:|------:|---------:|------:|---------:|
| 101251 | 302 | Barnet | 3021000 | Brookhill Nursery School                                    | Local authority nursery school | Local authority nursery school | Maintained School | OL  | 33.55 | 50.15 | 117   |   0 |  3925.35 |  1636 |  1636 |  2289.35 |  3611 |  314.35  |
| 101252 | 302 | Barnet | 3021001 | Hampden Way Nursery School                                  | Local authority nursery school | Local authority nursery school | Maintained School | OL  | 33.55 | 50.15 | 104   |   0 |  3489.2  |  1454 |  1454 |  2035.2  |  3300 |  189.2   |
| 101253 | 302 | Barnet | 3021002 | Moss Hall Nursery School                                    | Local authority nursery school | Local authority nursery school | Maintained School | OL  | 33.55 | 50.15 | 113   |   0 |  3791.15 |  1580 |  1580 |  2211.15 |  3549 |  242.15  |
| 101254 | 302 | Barnet | 3021003 | St Margaret's Nursery School                                | Local authority nursery school | Local authority nursery school | Maintained School | OL  | 33.55 | 50.15 | 128   |   0 |  4294.4  |  1789 |  1789 |  2505.4  |  3736 |  558.4   |
| 101258 | 302 | Barnet | 3022002 | Barnfield Primary School                                    | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 473   |   0 | 15869.1  |  6612 |  6612 |  9257.15 | 15596 |  273.15  |
| 101259 | 302 | Barnet | 3022003 | Bell Lane Primary School                                    | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 427   |   0 | 14325.9  |  5969 |  5969 |  8356.85 | 13728 |  597.85  |
| 101262 | 302 | Barnet | 3022007 | Brookland Junior School                                     | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 356   |   0 | 11943.8  |  4977 |  4977 |  6966.8  | 11176 |  767.8   |
| 101263 | 302 | Barnet | 3022008 | Brookland Infant and Nursery School                         | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 316   |   0 | 10601.8  |  4417 |  4417 |  6184.8  |  9588 | 1013.8   |
| 101264 | 302 | Barnet | 3022009 | Brunswick Park Primary and Nursery School                   | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 455   |   0 | 15265.2  |  6361 |  6361 |  8904.25 | 14258 | 1007.25  |
| 101265 | 302 | Barnet | 3022010 | Childs Hill School                                          | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 414   |   0 | 13889.7  |  5787 |  5787 |  8102.7  | 12421 | 1468.7   |
| 101266 | 302 | Barnet | 3022011 | Church Hill School                                          | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 207   |   0 |  6944.85 |  2894 |  2894 |  4050.85 |  7284 | -339.15  |
| 101269 | 302 | Barnet | 3022014 | Colindale Primary School                                    | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 720   |   0 | 24156    | 10065 | 10065 | 14091    | 22071 | 2085     |
| 101270 | 302 | Barnet | 3022015 | Coppetts Wood Primary School                                | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 279   |   0 |  9360.45 |  3900 |  3900 |  5460.45 |  8592 |  768.45  |
| 101271 | 302 | Barnet | 3022016 | Courtland School                                            | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 209   |   0 |  7011.95 |  2922 |  2922 |  4089.95 |  6631 |  380.95  |
| 101272 | 302 | Barnet | 3022017 | Cromer Road Primary School                                  | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 414   |   0 | 13889.7  |  5787 |  5787 |  8102.7  | 12701 | 1188.7   |
| 101274 | 302 | Barnet | 3022019 | Deansbrook Infant School                                    | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 299   |   0 | 10031.5  |  4180 |  4180 |  5851.45 |  9775 |  256.45  |
| 101275 | 302 | Barnet | 3022021 | Dollis Primary School                                       | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 256   |   0 | 19962.2  |  3579 |  3579 |  5009.8  | 18678 | 1284.25  |
| 101277 | 302 | Barnet | 3022023 | Edgware Primary School                                      | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 637   |   0 | 21371.3  |  8905 |  8905 | 12466.4  | 20203 | 1168.35  |
| 101278 | 302 | Barnet | 3022024 | Fairway Primary School and Children's Centre                | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 320   |   0 | 10736    |  4473 |  4473 |  6263    | 10242 |  494     |
| 101279 | 302 | Barnet | 3022025 | Foulds School                                               | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 316   |   0 | 10601.8  |  4417 |  4417 |  6184.8  |  9806 |  795.8   |
| 101280 | 302 | Barnet | 3022026 | Frith Manor Primary School                                  | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 606   |   0 | 20331.3  |  8471 |  8471 | 11860.3  | 20017 |  314.3   |
| 101281 | 302 | Barnet | 3022027 | Garden Suburb Junior School                                 | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 355   |   0 | 11910.2  |  4963 |  4963 |  6947.25 | 10958 |  952.25  |
| 101282 | 302 | Barnet | 3022028 | Garden Suburb Infant School                                 | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 255   |   0 |  8555.25 |  3565 |  3565 |  4990.25 |  8312 |  243.25  |
| 101283 | 302 | Barnet | 3022029 | Goldbeaters Primary School                                  | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 467   |   0 | 15667.9  |  6528 |  6528 |  9139.85 | 14662 | 1005.85  |
| 101285 | 302 | Barnet | 3022031 | Hollickwood Primary School                                  | Foundation school              | Foundation school              | Maintained School | OL  | 33.55 | 50.15 | 210   |   0 |  7045.5  |  2936 |  2936 |  4109.5  |  6786 |  259.5   |
| 101286 | 302 | Barnet | 3022032 | Holly Park Primary School                                   | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 539   |   0 | 18083.5  |  7535 |  7535 | 10548.4  | 17059 | 1024.45  |
| 101289 | 302 | Barnet | 3022036 | Livingstone Primary and Nursery School                      | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 299   |   0 | 10031.5  |  4180 |  4180 |  5851.45 |  9339 |  692.45  |
| 101290 | 302 | Barnet | 3022037 | Manorside Primary School                                    | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 296   |   0 |  9930.8  |  4138 |  4138 |  5792.8  | 10429 | -498.2   |
| 101293 | 302 | Barnet | 3022042 | Monkfrith Primary School                                    | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 361   |   0 | 12111.5  |  5046 |  5046 |  7065.55 | 10211 | 1900.55  |
| 101294 | 302 | Barnet | 3022043 | Moss Hall Junior School                                     | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 469   |   0 | 15735    |  6556 |  6556 |  9178.95 | 13728 | 2006.95  |
| 101295 | 302 | Barnet | 3022044 | Moss Hall Infant School                                     | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 357   |   0 | 11977.4  |  4991 |  4991 |  6986.35 | 10989 |  988.35  |
| 101296 | 302 | Barnet | 3022045 | Northside Primary School                                    | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 283   |   0 |  9494.65 |  3956 |  3956 |  5538.65 |  8841 |  653.65  |
| 101298 | 302 | Barnet | 3022054 | Woodridge Primary School                                    | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 209   |   0 |  7011.95 |  2922 |  2922 |  4089.95 |  7316 | -304.05  |
| 101299 | 302 | Barnet | 3022055 | Tudor Primary School                                        | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 248   |   0 |  8320.4  |  3467 |  3467 |  4853.4  |  8032 |  288.4   |
| 101301 | 302 | Barnet | 3022057 | Underhill School                                            | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 569.5 |   0 | 19106.7  |  7961 |  7961 | 11145.7  | 19238 | -131.275 |
| 101304 | 302 | Barnet | 3022060 | Whitings Hill Primary School                                | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 460   |   0 | 15433    |  6430 |  6430 |  9003    | 14289 | 1144     |
| 101309 | 302 | Barnet | 3022067 | Chalgrove Primary School                                    | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 247   |   0 |  8286.85 |  3453 |  3453 |  4833.85 |  7907 |  379.85  |
| 101311 | 302 | Barnet | 3022070 | Sunnyfields Primary School                                  | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 264   |   0 |  8857.2  |  3691 |  3691 |  5166.2  |  8094 |  763.2   |
| 101312 | 302 | Barnet | 3022071 | Queenswell Infant & Nursery School                          | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 265   |   0 |  8890.75 |  3704 |  3704 |  5186.75 |  8810 |   80.75  |
| 101313 | 302 | Barnet | 3022072 | Queenswell Junior School                                    | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 346   |   0 | 11608.3  |  4837 |  4837 |  6771.3  | 10833 |  775.3   |
| 101314 | 302 | Barnet | 3022073 | Danegrove Primary School                                    | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 | 627   |   0 | 21035.8  |  8765 |  8765 | 12270.9  | 20421 |  614.85  |
| 101315 | 302 | Barnet | 3023300 | All Saints' CofE Primary School NW2                         | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 190   |   0 |  6374.5  |  2656 |  2656 |  3718.5  |  6008 |  366.5   |
| 101316 | 302 | Barnet | 3023302 | Christ Church Primary School                                | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 232   |   0 |  7783.6  |  3243 |  3243 |  4540.6  |  7316 |  467.6   |
| 101317 | 302 | Barnet | 3023304 | Holy Trinity CofE Primary School                            | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 265   |   0 |  8890.75 |  3704 |  3704 |  5186.75 |  7969 |  921.75  |
| 101318 | 302 | Barnet | 3023305 | Monken Hadley CofE Primary School                           | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 141   |   0 |  4730.55 |  1971 |  1971 |  2759.55 |  4514 |  216.55  |
| 101319 | 302 | Barnet | 3023307 | St John's CofE Junior Mixed and Infant School               | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 240   |   0 |  8052    |  3355 |  3355 |  4697    |  7627 |  425     |
| 101321 | 302 | Barnet | 3023309 | St John's CofE Primary School                               | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 232   |   0 |  7783.6  |  3243 |  3243 |  4540.6  |  7316 |  467.6   |
| 101323 | 302 | Barnet | 3023311 | St Mary's CofE Primary School                               | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 470   |   0 | 15768.5  |  6570 |  6570 |  9198.5  | 15067 |  701.5   |
| 101324 | 302 | Barnet | 3023312 | St Mary's CofE Primary School, East Barnet                  | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 214   |   0 |  7179.7  |  2992 |  2992 |  4187.7  |  6631 |  548.7   |
| 101325 | 302 | Barnet | 3023313 | St Paul's CofE Primary School N11                           | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 218   |   0 |  7313.9  |  3047 |  3047 |  4266.9  |  6849 |  464.9   |
| 101326 | 302 | Barnet | 3023314 | St Paul's CofE Primary School NW7                           | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 208   |   0 |  6978.4  |  2908 |  2908 |  4070.4  |  6537 |  441.4   |
| 101327 | 302 | Barnet | 3023315 | St Andrew's CofE Voluntary Aided Primary School, Totteridge | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 210   |   0 |  7045.5  |  2936 |  2936 |  4109.5  |  6506 |  539.5   |
| 101328 | 302 | Barnet | 3023316 | Trent CofE Primary School                                   | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 210   |   0 |  7045.5  |  2936 |  2936 |  4109.5  |  6475 |  570.5   |
| 101329 | 302 | Barnet | 3023317 | All Saints' CofE Primary School N20                         | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 272   |   0 |  9125.6  |  3802 |  3802 |  5323.6  |  8498 |  627.6   |
| 101330 | 302 | Barnet | 3023500 | The Annunciation Catholic Infant School                     | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 190   |   0 |  6374.5  |  2656 |  2656 |  3718.5  |  6475 | -100.5   |
| 101331 | 302 | Barnet | 3023501 | Our Lady of Lourdes RC School                               | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 239   |   0 |  8018.45 |  3341 |  3341 |  4677.45 |  7316 |  702.45  |
| 101332 | 302 | Barnet | 3023502 | St Agnes RC School                                          | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 361   |   0 | 12111.5  |  5046 |  5046 |  7065.55 | 11611 |  500.55  |
| 101333 | 302 | Barnet | 3023504 | St Catherine's RC School                                    | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 501   |   0 | 16808.5  |  7004 |  7004 |  9804.55 | 15316 | 1492.55  |
| 101334 | 302 | Barnet | 3023506 | St Vincent's Catholic Primary School                        | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 316   |   0 | 10601.8  |  4417 |  4417 |  6184.8  | 10024 |  577.8   |
| 101335 | 302 | Barnet | 3023507 | St Theresa's Catholic Primary School                        | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 229   |   0 |  7682.95 |  3201 |  3201 |  4481.95 |  7316 |  366.95  |
| 101337 | 302 | Barnet | 3023509 | St Joseph's Catholic Primary School                         | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 562   |   0 | 18855.1  |  7856 |  7856 | 10999.1  | 17713 | 1142.1   |
| 101338 | 302 | Barnet | 3023510 | Sacred Heart Roman Catholic Primary School                  | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 402   |   0 | 13487.1  |  5620 |  5620 |  7867.1  | 13137 |  350.1   |
| 101339 | 302 | Barnet | 3023511 | Blessed Dominic Catholic Primary School                     | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 435   |   0 | 14594.2  |  6081 |  6081 |  8513.25 | 13666 |  928.25  |
| 101340 | 302 | Barnet | 3023512 | Rosh Pinah Primary School                                   | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 430   |   0 | 14426.5  |  6011 |  6011 |  8415.5  | 14226 |  200.5   |
| 101341 | 302 | Barnet | 3023513 | Menorah Primary School                                      | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 440   |   0 | 14762    |  6151 |  6151 |  8611    | 13666 | 1096     |
| 101342 | 302 | Barnet | 3023514 | The Annunciation RC Junior School                           | Voluntary aided school         | Voluntary aided school         | Maintained School | OL  | 33.55 | 50.15 | 221   |   0 |  7414.55 |  3089 |  3089 |  4325.55 |  6849 |  565.55  |
| 101345 | 302 | Barnet | 3024003 | Friern Barnet School                                        | Community school               | Community school               | Maintained School | OL  | 33.55 | 50.15 |   0   | 781 | 39167.2  | 16320 | 16320 | 22847.2  | 39619 | -451.85  |



label: S=N-R
labeled_formulas: S=N-R
output: {"Arithmetic-Relationship": ["S=N-R"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_115382___xlsx_fd609e8e3b4fb1c7a9e915a3c86b87ccef5cf673.xlsx___line_726