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 |
|------:|:--------------------------|--------:|------:|----:|--------:|----------:|----------:|----------:|------:|-----------------:|-----------------:|----:|-----------------:|----:|-----------------:|---------:|---------:|----:|
| 13001 | Vermillion 13-1           | 1258.61 |  1.25 |   5 | 15      |  83.9073  | 0.0833333 |  83.9907  | 66264 |      5.56556e+06 |      1.94405e+06 |   0 |      7.50961e+06 |   0 |      7.50961e+06 |  2851825 | 246002   |   5 |
| 13003 | Irene-Wakonda 13-3        |  293.87 |  0    |   0 | 12.704  |  23.132   | 0         |  23.132   | 66264 |      1.53282e+06 | 535415           |   0 |      2.06824e+06 |   0 |      2.06824e+06 |   978735 |  64740.9 |   0 |
| 14001 | Florence 14-1             |  288.01 |  0    |   0 | 12.6601 |  22.7495  | 0         |  22.7495  | 66264 |      1.50747e+06 | 526560           |   0 |      2.03403e+06 |   0 |      2.03403e+06 |   287333 |  44786   |   0 |
| 14002 | Henry 14-2                |  168    |  0    |   0 | 12      |  14       | 0         |  14       | 66264 | 927696           | 324044           |   0 |      1.25174e+06 |   0 |      1.25174e+06 |   251455 |  32407.4 |   0 |
| 14004 | Watertown 14-4            | 3867.9  | 10.75 |  43 | 15      | 257.86    | 0.716667  | 258.577   | 66264 |      1.71343e+07 |      5.98502e+06 |   0 |      2.31194e+07 |   0 |      2.31194e+07 |  9753335 | 665097   |  44 |
| 14005 | Waverly 14-5              |  253    |  0    |   0 | 12.3975 |  20.4073  | 0         |  20.4073  | 66264 |      1.35227e+06 | 472349           |   0 |      1.82462e+06 |   0 |      1.82462e+06 |   466073 |  49368.6 |   0 |
| 15001 | McIntosh 15-1             |  138    |  0    |   0 | 12      |  11.5     | 0         |  11.5     | 66264 | 762036           | 266179           |   0 |      1.02822e+06 |   0 |      1.02822e+06 |   309049 |  23101.6 |   0 |
| 15002 | McLaughlin 15-2           |  442.5  |  1.5  |   6 | 13.8187 |  32.0217  | 0.108548  |  32.1303  | 66264 |      2.12908e+06 | 743688           |   0 |      2.87277e+06 |   0 |      2.87277e+06 |   408725 |  43259.2 |   6 |
| 15003 | Smee 15-3                 |  198    |  0.25 |   1 | 12      |  16.5     | 0.0208333 |  16.5208  | 66264 |      1.09474e+06 | 382392           |   0 |      1.47713e+06 |   0 |      1.47713e+06 |    25342 |  15853.5 |   1 |
| 16001 | Custer 16-1               |  890.66 |  0.25 |   1 | 15      |  59.3773  | 0.0166667 |  59.394   | 66264 |      3.93569e+06 |      1.37474e+06 |   0 |      5.31042e+06 |   0 |      5.31042e+06 |  4825182 | 216977   |   1 |
| 17001 | Ethan 17-1                |  270.5  |  0.5  |   2 | 12.5288 |  21.5903  | 0.0399082 |  21.6303  | 66264 |      1.43331e+06 | 500654           |   0 |      1.93396e+06 |   0 |      1.93396e+06 |   334072 |  25660.7 |   2 |
| 17002 | Mitchell 17-2             | 2801.72 | 20.25 |  81 | 15      | 186.781   | 1.35      | 188.131   | 66264 |      1.24663e+07 |      4.35449e+06 |   0 |      1.68208e+07 |   0 |      1.68208e+07 |  6225955 | 287100   |  90 |
| 17003 | Mount Vernon 17-3         |  220.2  |  0    |   0 | 12.1515 |  18.1212  | 0         |  18.1212  | 66264 |      1.20079e+06 | 419434           |   0 |      1.62022e+06 |   0 |      1.62022e+06 |   482386 |  45067.5 |   0 |
| 18003 | Waubay 18-3               |  184    |  0    |   0 | 12      |  15.3333  | 0         |  15.3333  | 66264 |      1.01605e+06 | 354906           |   0 |      1.37095e+06 |   0 |      1.37095e+06 |   553541 |  45213.7 |   0 |
| 18005 | Webster Area 18-5         |  504    |  0.5  |   2 | 14.28   |  35.2941  | 0.035014  |  35.3291  | 66264 |      2.34105e+06 | 817729           |   0 |      3.15878e+06 |   0 |      3.15878e+06 |  1949416 | 179823   |   2 |
| 19004 | Deuel 19-4                |  519.25 |  1    |   4 | 14.3944 |  36.0731  | 0.0694716 |  36.1426  | 66264 |      2.39495e+06 | 836557           |   0 |      3.23151e+06 |   0 |      3.23151e+06 |  1762252 | 168113   |   4 |
| 20001 | Eagle Butte 20-1          |  318.84 |  0    |   0 | 12.8913 |  24.733   | 0         |  24.733   | 66264 |      1.63891e+06 | 572470           |   0 |      2.21138e+06 |   0 |      2.21138e+06 |   426256 |  40102.9 |   0 |
| 20003 | Timber Lake 20-3          |  334    |  0.25 |   1 | 13.005  |  25.6824  | 0.0192234 |  25.7017  | 66264 |      1.7031e+06  | 594891           |   0 |      2.29799e+06 |   0 |      2.29799e+06 |   403194 |  23298.9 |   1 |
| 21001 | Armour 21-1               |  180    |  0.5  |   2 | 12      |  15       | 0.0416667 |  15.0417  | 66264 | 996721           | 348155           |   0 |      1.34488e+06 |   0 |      1.34488e+06 |   387789 |  41084.6 |   2 |
| 21003 | Corsica-Stickney 21-3     |  258    |  0.5  |   2 | 12.435  |  20.7479  | 0.0402091 |  20.7881  | 66264 |      1.3775e+06  | 481162           |   0 |      1.85867e+06 |   0 |      1.85867e+06 |   929275 |  86478.1 |   2 |
| 22001 | Bowdle 22-1               |  118.26 |  0    |   0 | 12      |   9.855   | 0         |   9.855   | 66264 | 653032           | 228104           |   0 | 881136           |   0 | 881136           |   518388 |  55940   |   0 |
| 22005 | Edmunds Central 22-5      |  140    |  0.5  |   2 | 12      |  11.6667  | 0.0416667 |  11.7083  | 66264 | 775841           | 271001           |   0 |      1.04684e+06 |   0 |      1.04684e+06 |  1099678 |  50069   |   2 |
| 22006 | Ipswich Public 22-6       |  412.13 |  7.75 |  31 | 13.591  |  30.3238  | 0.570231  |  30.894   | 66264 |      2.04716e+06 | 715074           |   0 |      2.76224e+06 |   0 |      2.76224e+06 |  1817118 | 186000   |  38 |
| 23001 | Edgemont 23-1             |  158    |  0    |   0 | 12      |  13.1667  | 0         |  13.1667  | 66264 | 872476           | 304756           |   0 |      1.17723e+06 |   0 |      1.17723e+06 |   780411 |  37820   |   2 |
| 23002 | Hot Springs 23-2          |  730.52 |  1    |   4 | 15      |  48.7013  | 0.0666667 |  48.768   | 66264 |      3.23156e+06 |      1.12879e+06 |   0 |      4.36035e+06 |   0 |      4.36035e+06 |  2082104 | 163415   |   4 |
| 23003 | Oelrichs 23-3             |  128    |  0    |   0 | 12      |  10.6667  | 0         |  10.6667  | 66264 | 706816           | 246891           |   0 | 953707           |   0 | 953707           |   158963 |  20914.8 |   0 |
| 24004 | Faulkton Area 24-4        |  356    |  4    |  16 | 13.17   |  27.0311  | 0.303721  |  27.3349  | 66264 |      1.81132e+06 | 632693           |   0 |      2.44401e+06 |   0 |      2.44401e+06 |  1654597 |  91582   |  16 |
| 25001 | Big Stone City 25-1       |   70    |  0    |   0 | 12      |   5.83333 | 0         |   5.83333 | 66264 | 386540           | 135018           |   0 | 521559           |   0 | 521559           |   506660 |  27115.5 |   0 |
| 25004 | Milbank 25-4              |  978.98 | 11.5  |  46 | 15      |  65.2653  | 0.766667  |  66.032   | 66264 |      4.37555e+06 |      1.52838e+06 |   0 |      5.90392e+06 |   0 |      5.90392e+06 |  3004358 | 200772   |  46 |
| 26002 | Burke 26-2                |  227    |  0    |   0 | 12.2025 |  18.6027  | 0         |  18.6027  | 66264 |      1.23269e+06 | 430580           |   0 |      1.66327e+06 |   0 |      1.66327e+06 |   450554 |  35853.4 |   0 |
| 26004 | Gregory 26-4              |  384    |  0.25 |   1 | 13.38   |  28.6996  | 0.0186846 |  28.7182  | 66264 |      1.90299e+06 | 664713           |   0 |      2.5677e+06  |   0 |      2.5677e+06  |   811237 |  93608.6 |   1 |
| 27001 | Haakon 27-1               |  315    |  0.25 |   1 | 12.8625 |  24.4898  | 0.0194363 |  24.5092  | 66264 |      1.62408e+06 | 567291           |   0 |      2.19137e+06 |   0 |      2.19137e+06 |  1030612 |  97645.3 |   1 |
| 28001 | Castlewood 28-1           |  314    |  2.5  |  10 | 12.855  |  24.4263  | 0.194477  |  24.6208  | 66264 |      1.63147e+06 | 569873           |   0 |      2.20134e+06 |   0 |      2.20134e+06 |   651520 |  55499.9 |  13 |
| 28002 | Estelline 28-2            |  273    |  1.25 |   5 | 12.5475 |  21.7573  | 0.0996214 |  21.8569  | 66264 |      1.44833e+06 | 505901           |   0 |      1.95423e+06 |   0 |      1.95423e+06 |  1050965 |  90176.5 |   7 |
| 28003 | Hamlin 28-3               |  847    |  3.5  |  14 | 15      |  56.4667  | 0.233333  |  56.7     | 66264 |      3.75717e+06 |      1.31238e+06 |   0 |      5.06955e+06 |   0 |      5.06955e+06 |  1803846 | 158601   |  18 |
| 29004 | Miller 29-4               |  424.03 |  1.25 |   5 | 13.6802 |  30.9958  | 0.0913728 |  31.0872  | 66264 |      2.05996e+06 | 719545           |   0 |      2.77951e+06 |   0 |      2.77951e+06 |  2300496 | 136169   |   9 |
| 30001 | Hanson 30-1               |  391    |  4.5  |  18 | 13.4325 |  29.1085  | 0.335008  |  29.4435  | 66264 |      1.95105e+06 | 681500           |   0 |      2.63255e+06 |   0 |      2.63255e+06 |   866370 |  76048   |  18 |
| 30003 | Bridgewater -Emery 30-3   |  335    |  0.75 |   3 | 13.0125 |  25.7445  | 0.0576369 |  25.8021  | 66264 |      1.70975e+06 | 597216           |   0 |      2.30697e+06 |   0 |      2.30697e+06 |   900265 |  41381.8 |   4 |
| 31001 | Harding County 31-1       |  194.25 |  0    |   0 | 12      |  16.1875  | 0         |  16.1875  | 66264 |      1.07265e+06 | 374676           |   0 |      1.44733e+06 |   0 |      1.44733e+06 |   867228 |      0   |   0 |
| 33001 | Freeman 33-1              |  337.45 |  8.5  |  34 | 13.0309 |  25.8962  | 0.652297  |  26.5485  | 66264 |      1.75921e+06 | 614492           |   0 |      2.3737e+06  |   0 |      2.3737e+06  |  1026564 | 111593   |  38 |
| 33002 | Menno 33-2                |  283    |  6.25 |  25 | 12.6225 |  22.4203  | 0.495148  |  22.9154  | 66264 |      1.51847e+06 | 530401           |   0 |      2.04887e+06 |   0 |      2.04887e+06 |   709438 | 170802   |  36 |
| 33003 | Parkston 33-3             |  529    |  2.75 |  11 | 14.3235 |  36.9323  | 0.191992  |  37.1243  | 66264 |      2.46001e+06 | 859280           |   0 |      3.31929e+06 |   0 |      3.31929e+06 |  1110256 | 113538   |  11 |
| 33005 | Tripp-Delmont 33-5        |  143    |  1.5  |   6 | 12      |  11.9167  | 0.125     |  12.0417  | 66264 | 797929           | 278717           |   0 |      1.07665e+06 |   0 |      1.07665e+06 |   719916 | 182158   |   7 |
| 34002 | Highmore-Harrold 34-2     |  216    |  0    |   0 | 12.12   |  17.8218  | 0         |  17.8218  | 66264 |      1.18094e+06 | 412503           |   0 |      1.59345e+06 |   0 |      1.59345e+06 |  1453167 |  94794.9 |   0 |
| 35002 | Kadoka Area 35-2          |  314.42 |  0    |   0 | 12.8582 |  24.453   | 0         |  24.453   | 66264 |      1.62035e+06 | 565989           |   0 |      2.18634e+06 |   0 |      2.18634e+06 |   751330 |  89153.2 |   0 |
| 36002 | Wessington Springs 36-2   |  376.2  |  4.75 |  19 | 13.3215 |  28.2401  | 0.356566  |  28.5966  | 66264 |      1.89493e+06 | 661898           |   0 |      2.55683e+06 |   0 |      2.55683e+06 |  1173502 | 178554   |  19 |
| 37003 | Jones County 37-3         |  178    |  0    |   0 | 12      |  14.8333  | 0         |  14.8333  | 66264 | 982916           | 343333           |   0 |      1.32625e+06 |   0 |      1.32625e+06 |   616973 |  73657.1 |   0 |
| 38001 | Arlington 38-1            |  259    |  0.75 |   3 | 12.4425 |  20.8158  | 0.0602773 |  20.876   | 66264 |      1.38333e+06 | 483197           |   0 |      1.86653e+06 |   0 |      1.86653e+06 |  1022618 |  52252.7 |   3 |
| 38002 | De Smet 38-2              |  284    |  0    |   0 | 12.63   |  22.4861  | 0         |  22.4861  | 66264 |      1.49002e+06 | 520465           |   0 |      2.01049e+06 |   0 |      2.01049e+06 |  1117528 |  58511.7 |   1 |
| 38003 | Lake Preston 38-3         |  169    |  0.75 |   3 | 12      |  14.0833  | 0.0625    |  14.1458  | 66264 | 937360           | 327420           |   0 |      1.26478e+06 |   0 |      1.26478e+06 |   709437 |  35808   |   3 |
| 39001 | Chester 39-1              |  544    |  5.75 |  23 | 14.58   |  37.3114  | 0.394376  |  37.7058  | 66264 |      2.49854e+06 | 872739           |   0 |      3.37127e+06 |   0 |      3.37127e+06 |  1211111 |  97862.5 |  23 |
| 39002 | Madison Central 39-2      | 1129.62 |  5.75 |  23 | 15      |  75.308   | 0.383333  |  75.6913  | 66264 |      5.01561e+06 |      1.75195e+06 |   0 |      6.76757e+06 |   0 |      6.76757e+06 |  3482332 | 188923   |  27 |
| 39004 | Rutland 39-4              |  176    |  4    |  16 | 12      |  14.6667  | 0.333333  |  15       | 66264 | 993960           | 347190           |   0 |      1.34115e+06 |   0 |      1.34115e+06 |   371325 |  32311.3 |  16 |
| 39005 | Oldham-Ramona 39-5        |  154    |  3.75 |  15 | 12      |  12.8333  | 0.3125    |  13.1458  | 66264 | 871096           | 304274           |   0 |      1.17537e+06 |   0 |      1.17537e+06 |   538679 |  21125.7 |  18 |
| 40001 | Lead-Deadwood 40-1        |  725.56 |  2.5  |  10 | 15      |  48.3707  | 0.166667  |  48.5373  | 66264 |      3.21628e+06 |      1.12345e+06 |   0 |      4.33973e+06 |   0 |      4.33973e+06 |  5647306 | 131939   |  10 |
| 40002 | Spearfish 40-2            | 2361.48 |  2.75 |  11 | 15      | 157.432   | 0.183333  | 157.615   | 66264 |      1.04442e+07 |      3.64817e+06 |   0 |      1.40924e+07 |   0 |      1.40924e+07 |  6774829 | 303766   |  13 |
| 41002 | Harrisburg 41-2           | 5418.53 | 22.5  |  90 | 15      | 361.235   | 1.5       | 362.735   | 66264 |      2.40363e+07 |      8.39588e+06 |   0 |      3.24322e+07 |   0 |      3.24322e+07 | 12802314 | 642397   | 103 |
| 41004 | Lennox 41-4               | 1135.53 |  0.25 |   1 | 15      |  75.702   | 0.0166667 |  75.7187  | 66264 |      5.01742e+06 |      1.75259e+06 |   0 |      6.77001e+06 |   0 |      6.77001e+06 |  2432965 | 244048   |   1 |
| 41005 | Tea Area 41-5             | 2061.25 |  7.25 |  29 | 15      | 137.417   | 0.483333  | 137.9     | 66264 |      9.13781e+06 |      3.19184e+06 |   0 |      1.23296e+07 |   0 |      1.23296e+07 |  2796963 | 234238   |  29 |
| 42001 | Lyman 42-1                |  353    |  0    |   0 | 13.1475 |  26.8492  | 0         |  26.8492  | 66264 |      1.77914e+06 | 621453           |   0 |      2.40059e+06 |   0 |      2.40059e+06 |  1117017 |  77798   |   0 |
| 43001 | Canistota 43-1            |  219.13 |  1    |   4 | 12.1435 |  18.0451  | 0.0823488 |  18.1274  | 66264 |      1.2012e+06  | 419578           |   0 |      1.62077e+06 |   0 |      1.62077e+06 |   511238 |  40459.6 |   4 |
| 43002 | Montrose 43-2             |  236    |  2.75 |  11 | 12.27   |  19.2339  | 0.224124  |  19.458   | 66264 |      1.28937e+06 | 450376           |   0 |      1.73974e+06 |   0 |      1.73974e+06 |   465905 |  55046.4 |  11 |
| 43007 | McCook Central 43-7       |  398.68 |  1    |   4 | 13.4901 |  29.5535  | 0.0741284 |  29.6277  | 66264 |      1.96325e+06 | 685762           |   0 |      2.64901e+06 |   0 |      2.64901e+06 |   907646 |  80038.6 |   7 |
| 44001 | Eureka 44-1               |  148.2  |  0    |   0 | 12      |  12.35    | 0         |  12.35    | 66264 | 818361           | 285853           |   0 |      1.10421e+06 |   0 |      1.10421e+06 |   998160 |  40021   |   1 |
| 44002 | Leola 44-2                |  212    |  7.75 |  31 | 12.09   |  17.5352  | 0.641026  |  18.1762  | 66264 |      1.20443e+06 | 420706           |   0 |      1.62513e+06 |   0 |      1.62513e+06 |   703965 | 142804   |  31 |
| 45004 | Britton - Hecla 45-4      |  434.1  |  5.25 |  21 | 13.7558 |  31.5577  | 0.381659  |  31.9394  | 66264 |      2.11643e+06 | 739269           |   0 |      2.8557e+06  |   0 |      2.8557e+06  |  1968028 | 305679   |  22 |
| 45005 | Langford Area 45-5        |  213    |  1.25 |   5 | 12.0975 |  17.6069  | 0.103327  |  17.7103  | 66264 |      1.17355e+06 | 409922           |   0 |      1.58348e+06 |   0 |      1.58348e+06 |   991298 |  64291.4 |   5 |
| 46001 | Meade 46-1                | 3003.11 |  0    |   0 | 15      | 200.207   | 0         | 200.207   | 66264 |      1.32665e+07 |      4.634e+06   |   0 |      1.79005e+07 |   0 |      1.79005e+07 |  7371446 | 233130   |   2 |
| 46002 | Faith 46-2                |  184    |  0    |   0 | 12      |  15.3333  | 0         |  15.3333  | 66264 |      1.01605e+06 | 354906           |   0 |      1.37095e+06 |   0 |      1.37095e+06 |   276621 |  15162.2 |   0 |
| 47001 | White River 47-1          |  383    |  0.25 |   1 | 13.3725 |  28.6409  | 0.0186951 |  28.6596  | 66264 |      1.8991e+06  | 663355           |   0 |      2.56245e+06 |   0 |      2.56245e+06 |   299750 |  25754.4 |   1 |
| 48003 | Howard 48-3               |  339    |  2.75 |  11 | 13.0425 |  25.9919  | 0.210849  |  26.2028  | 66264 |      1.7363e+06  | 606491           |   0 |      2.34279e+06 |   0 |      2.34279e+06 |  1586250 | 220662   |  13 |
| 49001 | Baltic 49-1               |  522    |  2    |   8 | 14.415  |  36.2123  | 0.138744  |  36.351   | 66264 |      2.40877e+06 | 841382           |   0 |      3.25015e+06 |   0 |      3.25015e+06 |   749940 |  41821.4 |   8 |
| 49002 | Brandon Valley 49-2       | 4681.8  | 12    |  48 | 15      | 312.12    | 0.8       | 312.92    | 66264 |      2.07353e+07 |      7.24285e+06 |   0 |      2.79782e+07 |   0 |      2.79782e+07 |  9053868 | 698681   |  56 |
| 49003 | Dell Rapids 49-3          |  982.16 |  0.5  |   2 | 15      |  65.4773  | 0.0333333 |  65.5107  | 66264 |      4.341e+06   |      1.51631e+06 |   0 |      5.85731e+06 |   0 |      5.85731e+06 |  2138291 | 197796   |   4 |
| 49004 | Garretson 49-4            |  465.34 |  1.25 |   5 | 13.9901 |  33.2622  | 0.0893492 |  33.3516  | 66264 |      2.21001e+06 | 771956           |   0 |      2.98196e+06 |   0 |      2.98196e+06 |   945563 | 148826   |   5 |
| 49006 | Tri-Valley 49-6           |  987    |  8.25 |  33 | 15      |  65.8     | 0.55      |  66.35    | 66264 |      4.39662e+06 |      1.53574e+06 |   0 |      5.93236e+06 |   0 |      5.93236e+06 |  2487026 | 230581   |  33 |
| 49007 | West Central 49-7         | 1384    |  1    |   4 | 15      |  92.2667  | 0.0666667 |  92.3333  | 66264 |      6.11838e+06 |      2.13715e+06 |   0 |      8.25553e+06 |   0 |      8.25553e+06 |  2623367 | 206280   |   6 |
| 50003 | Flandreau 50-3            |  700.28 | 19.5  |  78 | 15      |  46.6853  | 1.3       |  47.9853  | 66264 |      3.1797e+06  |      1.11067e+06 |   0 |      4.29037e+06 |   0 |      4.29037e+06 |  1150337 | 106861   |  83 |
| 50005 | Colman-Egan 50-5          |  279.4  |  0.5  |   2 | 12.5955 |  22.1825  | 0.0396967 |  22.2222  | 66264 |      1.47253e+06 | 514356           |   0 |      1.98689e+06 |   0 |      1.98689e+06 |   604765 |  51788.5 |   7 |
| 51001 | Douglas 51-1              | 2758    |  1    |   4 | 15      | 183.867   | 0.0666667 | 183.933   | 66264 |      1.21882e+07 |      4.25733e+06 |   0 |      1.64455e+07 |   0 |      1.64455e+07 |  2907640 | 211245   |   7 |
| 51002 | Hill City 51-2            |  488.3  |  3.25 |  13 | 14.1623 |  34.479   | 0.229483  |  34.7085  | 66264 |      2.29992e+06 | 803363           |   0 |      3.10329e+06 |   0 |      3.10329e+06 |  3092766 | 152065   |  13 |
| 51003 | New Underwood 51-3        |  268    |  0.25 |   1 | 12.51   |  21.4229  | 0.019984  |  21.4428  | 66264 |      1.42089e+06 | 496317           |   0 |      1.91721e+06 |   0 |      1.91721e+06 |   342944 |  31250.3 |   1 |
| 51005 | Wall 51-5                 |  276    |  0    |   0 | 12.57   |  21.957   | 0         |  21.957   | 66264 |      1.45496e+06 | 508218           |   0 |      1.96318e+06 |   0 |      1.96318e+06 |   735988 |  68876.7 |   0 |
| 52001 | Bison 52-1                |  141    |  0    |   0 | 12      |  11.75    | 0         |  11.75    | 66264 | 778602           | 271966           |   0 |      1.05057e+06 |   0 |      1.05057e+06 |   601582 |  61820.6 |   0 |
| 52004 | Lemmon 52-4               |  252.92 |  0    |   0 | 12.3969 |  20.4019  | 0         |  20.4019  | 66264 |      1.35191e+06 | 472222           |   0 |      1.82413e+06 |   0 |      1.82413e+06 |   965000 | 103127   |   0 |
| 53001 | Gettysburg 53-1           |  224.51 |  0.25 |   1 | 12.1838 |  18.4269  | 0.020519  |  18.4474  | 66264 |      1.2224e+06  | 426984           |   0 |      1.64938e+06 |   0 |      1.64938e+06 |   747230 |  61820.2 |   1 |
| 54002 | Sisseton 54-2             |  918.56 |  2.25 |   9 | 15      |  61.2373  | 0.15      |  61.3873  | 66264 |      4.06777e+06 |      1.42087e+06 |   0 |      5.48864e+06 |   0 |      5.48864e+06 |  1918497 | 429725   |  12 |
| 54004 | Rosholt 54-4              |  241    |  2.75 |  11 | 12.3075 |  19.5816  | 0.223441  |  19.805   | 66264 |      1.31236e+06 | 458407           |   0 |      1.77077e+06 |   0 |      1.77077e+06 |   452610 |  24781.7 |  14 |
| 54006 | Summit 54-6               |  176    |  2    |   8 | 12      |  14.6667  | 0.166667  |  14.8333  | 66264 | 982916           | 343333           |   0 |      1.32625e+06 |   0 |      1.32625e+06 |   311687 |  38935   |   8 |
| 54007 | Wilmot 54-7               |  218    |  0    |   0 | 12.135  |  17.9646  | 0         |  17.9646  | 66264 |      1.1904e+06  | 415808           |   0 |      1.60621e+06 |   0 |      1.60621e+06 |   547093 |  68539.4 |   0 |
| 55004 | Woonsocket 55-4           |  251    |  0.25 |   1 | 12.3825 |  20.2705  | 0.0201898 |  20.2907  | 66264 |      1.34455e+06 | 469650           |   0 |      1.8142e+06  |   0 |      1.8142e+06  |   499529 |  42330.1 |   1 |
| 55005 | Sanborn Central 55-5      |  184    |  4.5  |  18 | 12      |  15.3333  | 0.375     |  15.7083  | 66264 |      1.0409e+06  | 363585           |   0 |      1.40448e+06 |   0 |      1.40448e+06 |   747278 |  40613.9 |  18 |
| 56002 | Doland 56-2               |  139    |  4.75 |  19 | 12      |  11.5833  | 0.395833  |  11.9792  | 66264 | 793788           | 277270           |   0 |      1.07106e+06 |   0 |      1.07106e+06 |   912654 |  30297.3 |  19 |
| 56004 | Redfield 56-4             |  560.15 |  0.25 |   1 | 14.7011 |  38.1025  | 0.0170055 |  38.1195  | 66264 |      2.52595e+06 | 882316           |   0 |      3.40827e+06 |   0 |      3.40827e+06 |  1611956 |  92421.8 |   2 |
| 56006 | Hitchcock-Tulare 56-6     |  219    |  5.75 |  23 | 12.1425 |  18.0358  | 0.473543  |  18.5094  | 66264 |      1.22651e+06 | 428418           |   0 |      1.65492e+06 |   0 |      1.65492e+06 |  1403444 |  75632.2 |  23 |
| 56007 | Northwestern Area 56-7    |  309    |  0    |   0 | 12.8175 |  24.1077  | 0         |  24.1077  | 66264 |      1.59747e+06 | 557997           |   0 |      2.15547e+06 |   0 |      2.15547e+06 |  1536952 |  68109.2 |   0 |
| 57001 | Stanley County 57-1       |  415    |  0    |   0 | 13.6125 |  30.4867  | 0         |  30.4867  | 66264 |      2.02017e+06 | 705646           |   0 |      2.72582e+06 |   0 |      2.72582e+06 |  1690486 |  31189   |   0 |
| 58003 | Agar-Blunt-Onida 58-3     |  265    |  1.5  |   6 | 12.4875 |  21.2212  | 0.12012   |  21.3413  | 66264 |      1.41416e+06 | 493967           |   0 |      1.90813e+06 |   0 |      1.90813e+06 |  2296062 | 128448   |   6 |
| 59002 | Winner 59-2               |  711    |  0.5  |   2 | 15      |  47.4     | 0.0333333 |  47.4333  | 66264 |      3.14312e+06 |      1.09789e+06 |   0 |      4.24102e+06 |   0 |      4.24102e+06 |  1724057 | 105983   |   2 |
| 59003 | Colome Consolidated 59-3  |  202    |  0    |   0 | 12.015  |  16.8123  | 0         |  16.8123  | 66264 |      1.11405e+06 | 389138           |   0 |      1.50319e+06 |   0 |      1.50319e+06 |   546045 |  26814.8 |   0 |
| 60001 | Centerville 60-1          |  283.13 |  0.25 |   1 | 12.6235 |  22.4288  | 0.0198044 |  22.4487  | 66264 |      1.48754e+06 | 519597           |   0 |      2.00714e+06 |   0 |      2.00714e+06 |   595199 |  50559.8 |   1 |
| 60003 | Marion 60-3               |  178.72 |  0.25 |   1 | 12      |  14.8933  | 0.0208333 |  14.9142  | 66264 | 988273           | 345204           |   0 |      1.33348e+06 |   0 |      1.33348e+06 |   829094 | 139196   |   4 |
| 60004 | Parker 60-4               |  477    |  4    |  16 | 14.0775 |  33.8839  | 0.284141  |  34.168   | 66264 |      2.26411e+06 | 790853           |   0 |      3.05496e+06 |   0 |      3.05496e+06 |   900038 |  61973.9 |  16 |
| 60006 | Viborg-Hurley 60-6        |  349.07 |  1.75 |   7 | 13.118  |  26.61    | 0.133404  |  26.7434  | 66264 |      1.77212e+06 | 619002           |   0 |      2.39112e+06 |   0 |      2.39112e+06 |   982381 |  71499.4 |   7 |
| 61001 | Alcester-Hudson 61-1      |  341.24 |  0.25 |   1 | 13.0593 |  26.13    | 0.0191434 |  26.1492  | 66264 |      1.73275e+06 | 605250           |   0 |      2.338e+06   |   0 |      2.338e+06   |   900672 |  74045.6 |   5 |
| 61002 | Beresford 61-2            |  704.48 |  7.75 |  31 | 15      |  46.9653  | 0.516667  |  47.482   | 66264 |      3.14635e+06 |      1.09902e+06 |   0 |      4.24537e+06 |   0 |      4.24537e+06 |  1414309 | 129467   |  31 |
| 61007 | Elk Point-Jefferson 61-7  |  696    |  1    |   4 | 15      |  46.4     | 0.0666667 |  46.4667  | 66264 |      3.07907e+06 |      1.07552e+06 |   0 |      4.15459e+06 |   0 |      4.15459e+06 |  1501175 | 104576   |   4 |
| 61008 | Dakota Valley 61-8        | 1379.3  |  5.25 |  21 | 15      |  91.9533  | 0.35      |  92.3033  | 66264 |      6.11639e+06 |      2.13646e+06 |   0 |      8.25285e+06 |   0 |      8.25285e+06 |  4206522 | 237738   |  21 |
| 62005 | Selby 62-5                |  166    |  0    |   0 | 12      |  13.8333  | 0         |  13.8333  | 66264 | 916652           | 320187           |   0 |      1.23684e+06 |   0 |      1.23684e+06 |  1231574 | 123717   |   0 |
| 62006 | Mobridge-Pollock 62-6     |  621.14 |  0    |   0 | 15      |  41.4093  | 0         |  41.4093  | 66264 |      2.74395e+06 | 958461           |   0 |      3.70241e+06 |   0 |      3.70241e+06 |  1139117 | 229278   |   0 |
| 63001 | Gayville-Volin 63-1       |  279    |  0.25 |   1 | 12.5925 |  22.156   | 0.0198531 |  22.1759  | 66264 |      1.46946e+06 | 513284           |   0 |      1.98275e+06 |   0 |      1.98275e+06 |   304607 |  36308.7 |   1 |
| 63003 | Yankton 63-3              | 2808.99 |  9.75 |  39 | 15      | 187.266   | 0.65      | 187.916   | 66264 |      1.24521e+07 |      4.34951e+06 |   0 |      1.68016e+07 |   0 |      1.68016e+07 |  6433081 | 586417   |  43 |
| 64002 | Dupree 64-2               |  397    |  0    |   0 | 13.4775 |  29.4565  | 0         |  29.4565  | 66264 |      1.95191e+06 | 681801           |   0 |      2.63371e+06 |   0 |      2.63371e+06 |   345998 |      0   |   0 |
| 65001 | Oglala Lakota County 65-1 | 1757.26 |  1.25 |   5 | 15      | 117.151   | 0.0833333 | 117.234   | 66264 |      7.7684e+06  |      2.7135e+06  |   0 |      1.04819e+07 |   0 |      1.04819e+07 |   130517 | 248921   |   5 |



label: G=C/F
H=D/F
I=G+H
K=I*J
N=K+L+M
labeled_formulas: G=C/F
H=D/F
I=G+H
K=I*J
O=A*M
O=C*M
O=F*M
O=G*M
O=I*M
O=J*M
P=K+L
O=K*M
O=L*M
O=M*N
P=M+N
O=M*P
O=M*Q
O=M*R
N=K+L+M
O=(A+C)*M
P=(E/A)+N
O=(A+F)*M
P=(F/A)+N
O=(A+G)*M
P=(G/A)+N
O=(A+I)*M
P=(I/A)+N
O=(A+J)*M
O=(A+K)*M
O=(A+L)*M
O=(A*M)*N
P=(A*M)+N
O=(A*M)*P
O=(A*M)*Q
O=(A*M)*R
P=(S/A)+N
O=(C+F)*M
output: {"Arithmetic-Relationship": ["G=C/F", "H=D/F", "I=G+H", "K=I*J", "N=K+L+M"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_615110___xlsx_5ef3f7120bca97720f4dec08b971458029fd9f4f.xlsx___line_363