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 |
|:-----------------------------|-----:|-----:|-----:|-----:|----:|-----:|----:|
| Kent                         | 2560 | 2560 | 2560 | 2172 | 388 | 2560 |  47 |
| Manchester                   | 2385 | 2385 | 2385 | 2273 | 112 | 2385 | 346 |
| Leeds                        | 2190 | 2190 | 2190 | 1894 | 296 | 2190 | 138 |
| Liverpool                    | 2105 | 2105 | 2105 | 1955 | 150 | 2105 |  14 |
| Norfolk                      | 1700 | 1700 | 1700 | 1654 |  46 | 1700 | 316 |
| Sheffield                    | 1680 | 1680 | 1680 | 1613 |  67 | 1680 | 127 |
| Hampshire                    | 1590 | 1590 | 1590 | 1409 | 181 | 1590 |   7 |
| Staffordshire                | 1390 | 1390 | 1390 | 1110 | 280 | 1390 | 182 |
| Devon                        | 1370 | 1370 | 1370 | 1253 | 117 | 1370 | 115 |
| Lincolnshire                 | 1370 | 1370 | 1370 | 1169 | 201 | 1370 | 171 |
| Bristol                      | 1355 | 1355 | 1355 | 1310 |  45 | 1355 |  34 |
| Hertfordshire                | 1350 | 1350 | 1350 | 1274 |  76 | 1350 |  10 |
| Durham                       | 1320 | 1320 | 1320 | 1259 |  61 | 1320 |  93 |
| Northamptonshire             | 1200 | 1200 | 1200 | 1032 | 168 | 1200 | 199 |
| Nottingham                   | 1200 | 1200 | 1200 | 1169 |  31 | 1200 |  95 |
| West Sussex                  | 1165 | 1165 | 1165 |  531 | 634 | 1165 | 143 |
| Suffolk                      | 1150 | 1150 | 1150 | 1082 |  68 | 1150 | 123 |
| Leicester                    | 1140 | 1140 | 1140 | 1002 | 138 | 1140 |  80 |
| Tower Hamlets                | 1120 | 1120 | 1120 | 1072 |  48 | 1120 |   1 |
| Sandwell                     | 1115 | 1115 | 1115 |  846 | 269 | 1115 |  36 |
| Southwark                    | 1085 | 1085 | 1085 |  992 |  93 | 1085 |  38 |
| Kingston upon Hull           | 1080 | 1080 | 1080 | 1067 |  13 | 1080 |   8 |
| Lambeth                      | 1080 | 1080 | 1080 |  789 | 291 | 1080 | 103 |
| Cumbria                      | 1050 | 1050 | 1050 |  997 |  53 | 1050 |  43 |
| Surrey                       | 1050 | 1050 | 1050 |  978 |  72 | 1050 |  38 |
| East Sussex                  | 1015 | 1015 | 1015 |  969 |  46 | 1015 |  48 |
| Newcastle upon Tyne          | 1010 | 1010 | 1010 |  929 |  81 | 1010 |   9 |
| Newham                       |  985 |  985 |  985 |  980 |   5 |  985 |   0 |
| Wakefield                    |  930 |  930 |  930 |  907 |  23 |  930 | 293 |
| Lewisham                     |  910 |  910 |  910 |  811 |  99 |  910 |   2 |
| Coventry                     |  905 |  905 |  905 |  874 |  31 |  905 |  37 |
| Gloucestershire              |  900 |  900 |  900 |  825 |  75 |  900 |  49 |
| Ealing                       |  880 |  880 |  880 |  812 |  68 |  880 |  56 |
| Doncaster                    |  870 |  870 |  870 |  751 | 119 |  870 | 426 |
| Somerset                     |  870 |  870 |  870 |  848 |  22 |  870 |  64 |
| Haringey                     |  850 |  850 |  850 |  698 | 152 |  850 |  87 |
| North Yorkshire              |  845 |  845 |  845 |  754 |  91 |  845 |  29 |
| Salford                      |  835 |  835 |  835 |  803 |  32 |  835 |   0 |
| Stoke-on-Trent               |  835 |  835 |  835 |  759 |  76 |  835 |  35 |
| Bolton                       |  830 |  830 |  830 |  729 | 101 |  830 |  31 |
| Islington                    |  815 |  815 |  815 |  755 |  60 |  815 |   2 |
| Brent                        |  810 |  810 |  810 |  544 | 266 |  810 | 102 |
| Leicestershire               |  810 |  810 |  810 |  758 |  52 |  810 | 125 |
| Oxfordshire                  |  810 |  810 |  810 |  624 | 186 |  810 |  87 |
| Wolverhampton                |  810 |  810 |  810 |  683 | 127 |  810 |  32 |
| Cambridgeshire               |  805 |  805 |  805 |  728 |  77 |  805 |  17 |
| Sunderland                   |  805 |  805 |  805 |  769 |  36 |  805 |   4 |
| Warwickshire                 |  805 |  805 |  805 |  770 |  35 |  805 |  33 |
| Walsall                      |  795 |  795 |  795 |  745 |  50 |  795 |  37 |
| Greenwich                    |  790 |  790 |  790 |  596 | 194 |  790 |  32 |
| Croydon                      |  785 |  785 |  785 |  660 | 125 |  785 |  35 |
| Enfield                      |  775 |  775 |  775 |  567 | 208 |  775 | 125 |
| Waltham Forest               |  760 |  760 |  760 |  728 |  32 |  760 |   0 |
| Camden                       |  755 |  755 |  755 |  738 |  17 |  755 |  30 |
| Wigan                        |  755 |  755 |  755 |  715 |  40 |  755 |   5 |
| Plymouth                     |  745 |  745 |  745 |  669 |  76 |  745 |  58 |
| Dudley                       |  740 |  740 |  740 |  700 |  40 |  740 |  31 |
| Rotherham                    |  730 |  730 |  730 |  631 |  99 |  730 |  65 |
| Barnet                       |  705 |  705 |  705 |  648 |  57 |  705 |   0 |
| Southampton                  |  685 |  685 |  685 |  649 |  36 |  685 |  17 |
| Oldham                       |  680 |  680 |  680 |  616 |  64 |  680 | 158 |
| Brighton and Hove            |  675 |  675 |  675 |  575 | 100 |  675 |  33 |
| Rochdale                     |  675 |  675 |  675 |  664 |  11 |  675 |  22 |
| Derby                        |  660 |  660 |  660 |  580 |  80 |  660 | 283 |
| Wandsworth                   |  660 |  660 |  660 |  622 |  38 |  660 |  26 |
| Northumberland               |  650 |  650 |  650 |  603 |  47 |  650 |  41 |
| Barking and Dagenham         |  645 |  645 |  645 |  518 | 127 |  645 |  70 |
| Barnsley                     |  645 |  645 |  645 |  572 |  73 |  645 |  40 |
| Westminster                  |  640 |  640 |  640 |  599 |  41 |  640 |  36 |
| Knowsley                     |  620 |  620 |  620 |  570 |  50 |  620 |  34 |
| Tameside                     |  620 |  620 |  620 |  460 | 160 |  620 | 223 |
| Gateshead                    |  595 |  595 |  595 |  449 | 146 |  595 |  76 |
| Dorset                       |  590 |  590 |  590 |  495 |  95 |  590 |  12 |
| Cheshire East                |  585 |  585 |  585 |  546 |  39 |  585 |  41 |
| Hounslow                     |  585 |  585 |  585 |  450 | 135 |  585 |  21 |
| Middlesbrough                |  570 |  570 |  570 |  511 |  59 |  570 |  36 |
| Stockport                    |  565 |  565 |  565 |  492 |  73 |  565 |  28 |
| Medway                       |  560 |  560 |  560 |  484 |  76 |  560 |  95 |
| Hillingdon                   |  555 |  555 |  555 |  192 | 363 |  555 |   2 |
| Portsmouth                   |  555 |  555 |  555 |  510 |  45 |  555 |  25 |
| Redbridge                    |  550 |  550 |  550 |  453 |  97 |  550 |   0 |
| Buckinghamshire              |  545 |  545 |  545 |  389 | 156 |  545 |   2 |
| Hammersmith and Fulham       |  540 |  540 |  540 |  498 |  42 |  540 |  45 |
| Cheshire West and Chester    |  525 |  525 |  525 |  496 |  29 |  525 |  97 |
| Luton                        |  525 |  525 |  525 |  422 | 103 |  525 |   3 |
| Wiltshire                    |  510 |  510 |  510 |  510 |   0 |  510 |  27 |
| East Riding of Yorkshire     |  505 |  505 |  505 |  403 | 102 |  505 |  32 |
| North East Lincolnshire      |  505 |  505 |  505 |  480 |  25 |  505 |  31 |
| Bromley                      |  490 |  490 |  490 |  487 |   3 |  490 |   0 |
| Calderdale                   |  475 |  475 |  475 |  399 |  76 |  475 |  27 |
| Blackburn with Darwen        |  465 |  465 |  465 |  454 |  11 |  465 |  90 |
| Shropshire                   |  455 |  455 |  455 |  404 |  51 |  455 |  20 |
| Stockton-on-Tees             |  455 |  455 |  455 |  438 |  17 |  455 |  25 |
| Peterborough                 |  450 |  450 |  450 |  371 |  79 |  450 |   6 |
| South Tyneside               |  450 |  450 |  450 |  415 |  35 |  450 |  11 |
| Southend-on-Sea              |  420 |  420 |  420 |  365 |  55 |  420 | 102 |
| Havering                     |  415 |  415 |  415 |  317 |  98 |  415 |   4 |
| Redcar and Cleveland         |  405 |  405 |  405 |  382 |  23 |  405 | 175 |
| Bexley                       |  400 |  400 |  400 |  394 |   6 |  400 |  73 |
| Kensington and Chelsea       |  400 |  400 |  400 |  370 |  30 |  400 |  31 |
| Harrow                       |  395 |  395 |  395 |  271 | 124 |  395 |  39 |
| Bury                         |  385 |  385 |  385 |  377 |   8 |  385 |  12 |
| Halton                       |  375 |  375 |  375 |  338 |  37 |  375 |   0 |
| Bournemouth                  |  370 |  370 |  370 |  350 |  20 |  370 |   9 |
| Merton                       |  370 |  370 |  370 |  349 |  21 |  370 |   2 |
| North Lincolnshire           |  365 |  365 |  365 |  278 |  87 |  365 |  87 |
| Telford and Wrekin           |  365 |  365 |  365 |  352 |  13 |  365 |  21 |
| Torbay                       |  365 |  365 |  365 |  346 |  19 |  365 |  20 |
| Thurrock                     |  360 |  360 |  360 |  306 |  54 |  360 |  59 |
| Trafford                     |  360 |  360 |  360 |  352 |   8 |  360 |  33 |
| Solihull                     |  355 |  355 |  355 |  326 |  29 |  355 |   8 |
| Slough                       |  330 |  330 |  330 |  295 |  35 |  330 |   0 |
| Sutton                       |  320 |  320 |  320 |  320 |   0 |  320 |   4 |
| Isle of Wight                |  315 |  315 |  315 |  220 |  95 |  315 |  53 |
| York                         |  315 |  315 |  315 |  271 |  44 |  315 |  41 |
| Herefordshire                |  310 |  310 |  310 |  267 |  43 |  310 |  68 |
| Central Bedfordshire         |  305 |  305 |  305 |  244 |  61 |  305 |   0 |
| North Somerset               |  305 |  305 |  305 |  272 |  33 |  305 |  44 |
| South Gloucestershire        |  295 |  295 |  295 |  285 |  10 |  295 |  13 |
| Hartlepool                   |  290 |  290 |  290 |  286 |   4 |  290 |   6 |
| Darlington                   |  275 |  275 |  275 |  262 |  13 |  275 |  23 |
| Poole                        |  240 |  240 |  240 |  230 |  10 |  240 |  21 |
| Kingston upon Thames         |  225 |  225 |  225 |  186 |  39 |  225 |   9 |
| Bath and North East Somerset |  215 |  215 |  215 |  182 |  33 |  215 |  43 |
| Richmond upon Thames         |  190 |  190 |  190 |  162 |  28 |  190 |  21 |
| West Berkshire               |  145 |  145 |  145 |  142 |   3 |  145 |  13 |
| Windsor and Maidenhead       |  140 |  140 |  140 |  110 |  30 |  140 |  51 |
| Bracknell Forest             |  115 |  115 |  115 |   98 |  17 |  115 |   6 |
| Wokingham                    |  110 |  110 |  110 |   85 |  25 |  110 |   0 |
| Rutland                      |   30 |   30 |   30 |   30 |   0 |   30 |   9 |
| City of London               |    3 |    3 |    3 |    3 |   0 |    3 |   0 |
| Isles of Scilly              |    2 |    2 |    2 |    2 |   0 |    2 |   0 |



labeled_formulas: F=B-E
F=C-E
F=D-E
G=(B+C)-D
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_739011___xlsx_7786aedc029416a81e078ea285b3c0cc7a57e910.xlsx___line_322