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 |
|:--------------------------|------:|---------:|---------:|---------:|---------:|---------:|---------:|---------:|---------:|---------:|---------:|---------:|---------:|---------:|-----------------:|-------------:|
| Aberdeen 06-1             |  6001 |  8856836 |  8607562 |  7487957 |  6449086 |  8546142 |  8336649 |  7332556 |  6677612 |  6039208 |  5142062 |  7250657 |  8254642 |  5142062 |      3.00714e+07 |  0.170995    |
| Agar-Blunt-Onida 58-3     | 58003 |  2803186 |  2544180 |  2324884 |  2140866 |  2553088 |  2467942 |  2370199 |  2388321 |  2343243 |  2209498 |  2829933 |  3072737 |  2140866 |      3.0602e+06  |  0.699583    |
| Alcester-Hudson 61-1      | 61001 |   994804 |   903638 |   772920 |   647207 |   753287 |   730343 |   609932 |   530501 |   480183 |   428396 |   739673 |   965640 |   428396 |      2.95594e+06 |  0.144927    |
| Andes Central 11-1        | 11001 |   179716 |   102337 |   579010 |   370443 |   383952 |   709721 |   461461 |   251542 |    26760 |    77468 |   208030 |   103844 |    26760 |      4.66974e+06 |  0.00573051  |
| Arlington 38-1            | 38001 |  1102983 |  1024329 |   894919 |   741194 |   930397 |   881646 |   750116 |   661150 |   556802 |   469049 |   951489 |   947043 |   469049 |      2.56342e+06 |  0.182978    |
| Armour 21-1               | 21001 |   726236 |   692849 |   601846 |   512595 |   558242 |   500807 |   438564 |   403182 |   320505 |   284687 |   486865 |   592757 |   284687 |      1.89554e+06 |  0.150188    |
| Avon 04-1                 |  4001 |   629728 |   597580 |   530167 |   480382 |   568018 |   555554 |   494172 |   453505 |   404765 |   352406 |   473060 |   777709 |   352406 |      2.0589e+06  |  0.171162    |
| Baltic 49-1               | 49001 |   966743 |   969355 |   887140 |   823404 |   858076 |   892149 |   811788 |   818291 |   790174 |   743368 |   913763 |  1010241 |   743368 |      3.41997e+06 |  0.217361    |
| Belle Fourche 09-1        |  9001 |  1873706 |  1903270 |  1402665 |  1160796 |  1769304 |  1789429 |  1461397 |  1367299 |  1367515 |  1271241 |  2006397 |  2007713 |  1160796 |      9.55264e+06 |  0.121516    |
| Bennett County 03-1       |  3001 |   388446 |   441412 |   465775 |   376750 |   279484 |    90654 |     4976 |   217554 |    85269 |   -71084 |   -46722 |   321750 |   -71084 |      5.24432e+06 | -0.0135545   |
| Beresford 61-2            | 61002 |  1298027 |  1009945 |   843760 |   733711 |  1176980 |  1132591 |   945377 |   863229 |   792845 |   726439 |  1229237 |  1178060 |   726439 |      4.88492e+06 |  0.14871     |
| Big Stone City 25-1       | 25001 |   461381 |   440032 |   394085 |   330932 |   429746 |   461925 |   394904 |   352630 |   346165 |   257369 |   338441 |   489652 |   257369 |      1.25079e+06 |  0.205765    |
| Bison 52-1                | 52001 |   414003 |   486395 |   414418 |   287484 |   448597 |   374931 |   406867 |   294688 |   266441 |   201790 |   352579 |   348993 |   201790 |      1.88648e+06 |  0.106967    |
| Bon Homme 04-2            |  4002 |   166147 |   131731 |    14453 |     8195 |   137513 |     4103 |    15263 |    25661 |     2129 |     7341 |   260271 |    57177 |     2129 |      4.45354e+06 |  0.000478046 |
| Bowdle 22-1               | 22001 |   289084 |   210089 |   123552 |    58983 |   260251 |   234937 |   157123 |    80546 |    28436 |   215988 |   451796 |   363512 |    28436 |      1.42191e+06 |  0.0199985   |
| Brandon Valley 49-2       | 49002 |  6783942 |  3851456 |  3786327 |  1730976 |  3612891 |  5410027 |  4682673 |  4830114 |  5120513 |  4781480 |  7666715 |  7300702 |  1730976 |      2.72059e+07 |  0.063625    |
| Bridgewater-Emery 30-3    | 30003 |  1076986 |  1050530 |   965162 |   878596 |  1146622 |  1129012 |  1037449 |   972593 |   884900 |   789927 |  1119010 |  1182445 |   789927 |      2.81741e+06 |  0.280373    |
| Britton-Hecla 45-4        | 45004 |   548217 |   406192 |   264955 |   110456 |   543267 |   461165 |   298284 |    87678 |    22364 |   163753 |   650745 |   856788 |    22364 |      3.4582e+06  |  0.00646694  |
| Brookings 05-1            |  5001 |  5622988 |  5156334 |  4226527 |  3299694 |  5653331 |  5156549 |  4579146 |  4429523 |  3650261 |  3262586 |  6487677 |  6248964 |  3262586 |      2.28705e+07 |  0.142655    |
| Burke 26-2                | 26002 |   461699 |   431570 |   370981 |   287408 |   515250 |   515225 |   485082 |   477811 |   390381 |   368475 |   569202 |   573050 |   287408 |      2.50464e+06 |  0.11475     |
| Canistota 43-1            | 43001 |   680683 |   639961 |   552986 |   536847 |   677572 |   646318 |   569737 |   514411 |   462805 |   394527 |   519546 |   586344 |   394527 |      2.06689e+06 |  0.19088     |
| Canton 41-1               | 41001 |  1994560 |  1908335 |  1581584 |  1374417 |  1888657 |  1757605 |  1524971 |  1475979 |  1413942 |  1289215 |  1958741 |  2038613 |  1289215 |      5.73345e+06 |  0.224858    |
| Castlewood 28-1           | 28001 |   672253 |   620346 |   511162 |   460551 |   571550 |   548789 |   513404 |   463967 |   384593 |   355098 |   515927 |   569105 |   355098 |      2.39797e+06 |  0.148083    |
| Centerville 60-1          | 60001 |   684126 |   633630 |   535520 |   499247 |   658437 |   668393 |   608677 |   606067 |   581260 |   562787 |   717014 |   692959 |   499247 |      2.13911e+06 |  0.23339     |
| Chamberlain 07-1          |  7001 |   133522 |    62568 |  -308197 |  -553996 |  -396717 |  -586206 |  -915493 |  -983288 | -1214850 | -1427535 |  -337443 |  -296095 | -1427535 |      8.2885e+06  | -0.172231    |
| Chester Area 39-1         | 39001 |  1197592 |  1116254 |   980640 |   870640 |  1038252 |   953888 |   811094 |   738379 |   632671 |   555753 |   897553 |  1108587 |   555753 |      3.92207e+06 |  0.141699    |
| Clark 12-2                | 12002 |  1166276 |  1049221 |   866678 |   614959 |  1166257 |  1123832 |   983209 |   930633 |   780113 |   627222 |  1297058 |  1227990 |   614959 |      3.22595e+06 |  0.190629    |
| Colman-Egan 50-5          | 50005 |   464275 |   432651 |   386925 |   333876 |   415999 |   394356 |   344914 |   346872 |   302261 |   243033 |   415252 |   390578 |   243033 |      2.02289e+06 |  0.120141    |
| Colome Consolidated 59-3  | 59003 |   560275 |   524538 |   476205 |   416116 |   472484 |   505921 |   417023 |   413067 |   342585 |   314994 |   440498 |   869894 |   314994 |      2.03965e+06 |  0.154435    |
| Corsica-Stickney 21-3     | 21003 |  1128921 |  1070224 |   961594 |   856357 |  1025683 |   962289 |   827619 |   811402 |   725808 |   628541 |   867343 |  1341601 |   628541 |      2.47871e+06 |  0.253576    |
| Custer 16-1               | 16001 |  1775447 |  1665626 |  1190261 |   803527 |  1554637 |  1487147 |  1160187 |   754601 |   321394 |   299128 |  1251808 |  2168319 |   299128 |      7.34163e+06 |  0.0407441   |
| Dakota Valley 61-8        | 61008 |  1901807 |  1657107 |  1128808 |   702446 |  1787215 |  1639135 |  1235079 |  1017213 |   780549 |   613593 |  2262018 |  2140745 |   613593 |      9.19226e+06 |  0.0667511   |
| De Smet 38-2              | 38002 |  1176388 |  1054581 |   909401 |   769456 |  1027111 |   952048 |   746238 |   650616 |   553783 |   529558 |   905147 |  1296325 |   529558 |      2.81984e+06 |  0.187797    |
| Dell Rapids 49-3          | 49003 |  1475890 |  1427924 |  1204062 |   984685 |  1254468 |  1392171 |  1159140 |  1023473 |  1001727 |   882091 |  1406053 |  1675131 |   882091 |      6.49497e+06 |  0.135811    |
| Deubrook Area 05-6        |  5006 |  1771305 |  1716485 |  1554933 |  1380291 |  1584781 |  1573842 |  1418848 |  1301708 |  1139150 |  1026696 |  1698137 |  1825293 |  1026696 |      3.43123e+06 |  0.299221    |
| Deuel 19-4                | 19004 |  1631896 |  1643888 |  1478828 |  1299046 |  1490300 |  1656045 |  1484281 |  1377485 |  1247621 |  1100278 |  1416752 |  1586072 |  1100278 |      3.71204e+06 |  0.296408    |
| Doland 56-2               | 56002 |   785904 |   701461 |   575667 |   485417 |   778745 |   730816 |   735727 |   652322 |   566005 |   527236 |   835512 |   788534 |   485417 |      1.69649e+06 |  0.286131    |
| Douglas 51-1              | 51001 |  1969468 |  1847491 |  1505975 |  1077665 |  1218382 |   958268 |   426358 |   358711 |    11786 |  -321180 |   361266 |  1870274 |  -321180 |      2.04014e+07 | -0.0157431   |
| Dupree 64-2               | 64002 |   426973 |   399785 |   173177 |   -87992 |  -224634 |  -409652 |  -558968 |  -706538 |  -759301 |  -566969 |  -660495 |   411287 |  -759301 |      4.73689e+06 | -0.160295    |
| Eagle Butte 20-1          | 20001 |   172394 |  -445213 |   337172 |    28554 |  -520722 |  -211332 |  -118011 |   189312 |   222155 |   -92212 |  -337999 |   107582 |  -520722 |      5.99128e+06 | -0.0869133   |
| Edgemont 23-1             | 23001 |   571735 |   637219 |   522849 |   443526 |   636152 |   611585 |   623584 |   549827 |   519784 |   456220 |   791771 |   837867 |   443526 |      1.65087e+06 |  0.268662    |
| Edmunds Central 22-5      | 22005 |   871151 |   871003 |   705685 |   596711 |   838435 |   812805 |   760078 |   675590 |   616806 |   795745 |  1108642 |   994851 |   596711 |      1.86532e+06 |  0.319897    |
| Elk Mountain 16-2         | 16002 |   333061 |   319578 |   296385 |   306438 |   285803 |   309492 |   308700 |   289049 |   267600 |   249901 |   239937 |   354389 |   239937 | 289388           |  0.829119    |
| Elk Point-Jefferson 61-7  | 61007 |  1139783 |  1049026 |   848053 |   739122 |  1071958 |  1053655 |   901897 |   872322 |   811710 |   734807 |  1170062 |  1379927 |   734807 |      4.55946e+06 |  0.161161    |
| Elkton 05-3               |  5003 |   505700 |   348695 |   150490 |   -44361 |   601565 |   441497 |   345045 |   239634 |   163329 |   -31214 |   716834 |   619359 |   -44361 |      2.98024e+06 | -0.0148851   |
| Estelline 28-2            | 28002 |   352753 |   245719 |   119962 |    16416 |   198061 |   165338 |    48493 |    -6781 |   140721 |    68753 |   477036 |   475133 |    -6781 |      2.43783e+06 | -0.00278157  |
| Ethan 17-1                | 17001 |   739974 |   690853 |   614132 |   498613 |   589560 |   650238 |   620625 |   596300 |   585681 |   567007 |   701939 |   721102 |   498613 |      2.00536e+06 |  0.24864     |
| Eureka 44-1               | 44001 |   697911 |   614193 |   471444 |   351398 |   511518 |   496389 |   460417 |   376993 |   262873 |   552611 |   761701 |   981694 |   262873 |      1.90857e+06 |  0.137733    |
| Faith 46-2                | 46002 |   640091 |   633348 |   597797 |   521764 |   548456 |   593607 |   678115 |   676334 |   700114 |   677175 |   725320 |   744237 |   521764 |      1.48066e+06 |  0.352386    |
| Faulkton Area 24-4        | 24004 |  1424429 |  1340520 |  1149489 |   925741 |  1420975 |  1354330 |  1198989 |  1095835 |   929212 |   851906 |  1419158 |  1577075 |   851906 |      2.83973e+06 |  0.299996    |
| Flandreau 50-3            | 50003 |  1440963 |  1292682 |  1166536 |   990485 |  1186709 |  1107714 |   926098 |   915492 |   808842 |   737935 |  1035485 |  1532185 |   737935 |      5.03218e+06 |  0.146643    |
| Florence 14-1             | 14001 |   838601 |   812427 |   746034 |   680948 |   745330 |   728525 |   693911 |   684979 |   627510 |   475764 |   547186 |   814845 |   475764 |      2.06472e+06 |  0.230425    |
| Frederick Area 06-2       |  6002 |   785076 |   724466 |   614396 |   510456 |   687216 |   651030 |   580050 |   508704 |   635399 |   551885 |   682443 |   945076 |   508704 |      1.8509e+06  |  0.274841    |
| Freeman 33-1              | 33001 |   613225 |   550944 |   399706 |   292162 |   824004 |   809154 |   662031 |   642430 |   526467 |   464221 |  1018638 |  1098803 |   292162 |      2.98018e+06 |  0.0980351   |
| Garretson 49-4            | 49004 |   913788 |   914775 |   806430 |   695673 |   941083 |  1052511 |  1058651 |  1009452 |  1016674 |   946664 |  1320238 |  1385903 |   695673 |      3.53897e+06 |  0.196575    |
| Gayville-Volin 63-1       | 63001 |   778501 |   701078 |   664359 |   611750 |   745664 |   759138 |   747808 |   732386 |   726485 |   718514 |   816313 |   825353 |   611750 |      2.15421e+06 |  0.283978    |
| Gettysburg 53-1           | 53001 |   727204 |   701235 |   631658 |   545325 |   665733 |   595747 |   532644 |   525365 |   446736 |   397910 |   558664 |   717056 |   397910 |      2.12931e+06 |  0.186873    |
| Gregory 26-4              | 26004 |   823387 |   909541 |   777866 |   673302 |   833864 |   799185 |   700552 |   672924 |   615075 |   644074 |   850502 |  1016260 |   615075 |      3.06517e+06 |  0.200666    |
| Groton Area 06-6          |  6006 |  1497953 |  1541226 |  1083252 |   738134 |  1568414 |  1558272 |  1190864 |   956336 |   703967 |   463716 |  1193933 |  1212198 |   463716 |      4.92221e+06 |  0.0942089   |
| Haakon 27-1               | 27001 |  1039883 |   987364 |   859078 |   713927 |   893116 |   842707 |   831994 |   723033 |   743861 |   672885 |   918136 |   821398 |   672885 |      2.69808e+06 |  0.249394    |
| Hamlin 28-3               | 28003 |  1840347 |  1721160 |  1538186 |  1385634 |  1721387 |  1731247 |  1574473 |  1549004 |  1430906 |  1135711 |  1907219 |  2121815 |  1135711 |      5.13697e+06 |  0.221086    |
| Hanson 30-1               | 30001 |   928041 |   899345 |   817365 |   747525 |   953807 |   926249 |   862992 |   856012 |   804161 |   751231 |   962302 |   941216 |   747525 |      2.90633e+06 |  0.257206    |
| Harding County 31-1       | 31001 |    52163 |    75898 |  -108380 |  -354994 |  -299877 |  -334003 |  -429613 |  -546679 |  -608953 |  -736649 |  -161201 |    81444 |  -736649 |      2.85724e+06 | -0.257818    |
| Harrisburg 41-2           | 41002 |  7754328 |  6816851 |  5433170 |  6118451 |  9367572 |  8468644 |  7123183 |  6687628 |  6112898 |  5176601 |  9363452 |  8579286 |  5176601 |      3.3365e+07  |  0.155151    |
| Henry 14-2                | 14002 |   257206 |   221442 |   137205 |    68251 |   177673 |   176195 |   136469 |   109483 |    72624 |    42990 |   195762 |   373523 |    42990 |      1.82633e+06 |  0.023539    |
| Herreid 10-1              | 10001 |   486997 |   477931 |   365143 |   279938 |   394593 |   521501 |   428815 |   389420 |   325504 |   445613 |   674510 |   515070 |   279938 |      1.41884e+06 |  0.1973      |
| Highmore-Harrold 34-2     | 34002 |  1064022 |   904735 |   740728 |   553788 |   807318 |   743829 |   655775 |   574926 |   438395 |   309604 |   637524 |   577686 |   309604 |      2.48944e+06 |  0.124367    |
| Hill City 51-2            | 51002 |   523237 |   305667 |   -18078 |  -424915 |    50290 |      652 |  -236708 |  -387538 |  -619910 |  -827450 |    45750 |   836901 |  -827450 |      4.42215e+06 | -0.187115    |
| Hitchcock-Tulare 56-6     | 56006 |   736879 |   586484 |   445945 |   302172 |   671647 |   592859 |   418268 |   286408 |   194635 |   374308 |   730136 |   700797 |   194635 |      2.34008e+06 |  0.0831746   |
| Hot Springs 23-2          | 23002 |   339856 |   509566 |   296518 |   237895 |   586670 |   517071 |   430919 |   366562 |   316151 |   252544 |   883342 |   986733 |   237895 |      5.12737e+06 |  0.046397    |
| Hoven 53-2                | 53002 |  1147555 |  1065918 |   947585 |   809677 |  1067685 |  1028818 |   980479 |   961686 |   884593 |   806301 |  1171555 |  1238716 |   806301 |      1.76642e+06 |  0.456459    |
| Howard 48-3               | 48003 |   733831 |   619009 |   425602 |   243194 |   480621 |   360433 |   169783 |    43481 |    15936 |    62257 |   372001 |   528362 |    15936 |      3.36976e+06 |  0.00472912  |
| Huron 02-2                |  2002 |  3563400 |  3752323 |  3364519 |  2999389 |  3901395 |  3704178 |  3297388 |  3129848 |  2850654 |  2552102 |  3376172 |  3915874 |  2552102 |      2.00608e+07 |  0.127218    |
| Ipswich Public 22-6       | 22006 |   953475 |   741461 |   552125 |   422719 |   835383 |   789463 |   537569 |   384776 |   272378 |   174970 |   683237 |   850616 |   174970 |      3.55986e+06 |  0.0491508   |
| Irene-Wakonda 13-3        | 13003 |  1188118 |  1187806 |  1055073 |   939693 |  1197043 |  1119448 |   992023 |   914191 |   840453 |   743712 |  1055706 |  1189827 |   743712 |      2.73159e+06 |  0.272263    |
| Iroquois 02-3             |  2003 |  1202208 |  1047610 |   907870 |   734412 |   983464 |   881973 |   708559 |   558241 |   505577 |   680592 |  1186853 |  1357786 |   505577 |      2.48062e+06 |  0.20381     |
| Jones County 37-3         | 37003 |   667528 |   623104 |   555491 |   506361 |   580301 |   586670 |   617275 |   590865 |   501351 |   453425 |   579324 |   645534 |   453425 |      1.85882e+06 |  0.243931    |
| Kadoka Area 35-2          | 35002 |   870207 |   803979 |   466915 |   357404 |   453865 |   425067 |   397818 |   334216 |   243825 |   132535 |   308602 |   545346 |   132535 |      3.9903e+06  |  0.0332143   |
| Kimball 07-2              |  7002 |   758835 |   700822 |   633030 |   530204 |   665196 |   610397 |   495646 |   404098 |   379424 |   382471 |   638257 |   670848 |   379424 |      2.6352e+06  |  0.143983    |
| Lake Preston 38-3         | 38003 |   830298 |   826375 |   705369 |   588260 |   961717 |   900521 |   789364 |   702469 |   618901 |   568817 |   984260 |  1204405 |   568817 |      2.08218e+06 |  0.273183    |
| Langford Area 45-5        | 45005 |   749257 |   704061 |   619197 |   507867 |   749929 |   758654 |   647189 |   581289 |   542340 |   466597 |   715803 |   911056 |   466597 |      1.87756e+06 |  0.248513    |
| Lead-Deadwood 40-1        | 40001 |  3145361 |  2742691 |  2243762 |  1774360 |  2924835 |  2617876 |  2136929 |  1843368 |  1692935 |  1368395 |  2856354 |  3400295 |  1368395 |      7.81045e+06 |  0.175201    |
| Lemmon 52-4               | 52004 |    17316 |   152742 |    11780 |  -116779 |    48099 |    67789 |    -1379 |  -110634 |  -125261 |  -248255 |   -37849 |   150295 |  -248255 |      2.57697e+06 | -0.0963358   |
| Lennox 41-4               | 41004 |  1856130 |  1718350 |  1480068 |  1062429 |  1781127 |  1729909 |  1468067 |  1349054 |  1340957 |  1244345 |  2048966 |  1872607 |  1062429 |      6.94774e+06 |  0.152917    |
| Leola 44-2                | 44002 |   207106 |   179323 |    46712 |   -50560 |   112019 |    57040 |    48647 |   -52432 |  -150688 |  -232117 |    60342 |   443137 |  -232117 |      2.27158e+06 | -0.102183    |
| Lyman 42-1                | 42001 |   749365 |   690552 |   604083 |   612401 |   777692 |   628184 |   555891 |   607391 |   461604 |   395359 |   649726 |   441673 |   395359 |      4.25026e+06 |  0.0930199   |
| Madison Central 39-2      | 39002 |  2808122 |  2657453 |  2319581 |  2045068 |  2838539 |  2597067 |  2196517 |  2045171 |  1836722 |  1742425 |  2841419 |  2799364 |  1742425 |      7.98631e+06 |  0.218176    |
| Marion 60-3               | 60003 |   889620 |   842846 |   756955 |   636961 |   766799 |   734380 |   614751 |   522926 |   395832 |   283232 |   493363 |   740743 |   283232 |      2.08287e+06 |  0.135982    |
| McCook Central 43-7       | 43007 |   875072 |   815564 |   680644 |   298538 |   803682 |   784212 |   666934 |   617634 |   405655 |   366276 |   809983 |   869513 |   298538 |      3.17572e+06 |  0.0940063   |
| McIntosh 15-1             | 15001 |   165580 |    88948 |    54305 |    88000 |   108627 |   129359 |   322841 |   264260 |   114234 |   110263 |   236466 |   277807 |    54305 |      3.08326e+06 |  0.0176129   |
| McLaughlin 15-2           | 15002 |  -275539 |    57548 |  -185884 |  -464554 |  -783655 |  -951729 |  -888710 | -1037030 | -1273601 | -1254078 | -1567370 |  -441479 | -1567370 |      6.02123e+06 | -0.260307    |
| Meade 46-1                | 46001 |  5536624 |  5416752 |  4907167 |  4325238 |  5510197 |  5853918 |  5273653 |  4959409 |  4579037 |  4201984 |  5415082 |  5876182 |  4201984 |      1.88397e+07 |  0.223039    |
| Menno 33-2                | 33002 |   972999 |   923376 |   771164 |   644890 |   800156 |   727144 |   636549 |   565177 |   437295 |   342615 |   478097 |  1203018 |   342615 |      2.79995e+06 |  0.122364    |
| Milbank 25-4              | 25004 |  3025215 |  2859230 |  2485417 |  1952817 |  2801883 |  2736160 |  2403306 |  2145929 |  1741884 |  1295376 |  1786049 |  3043910 |  1295376 |      7.23278e+06 |  0.179098    |
| Miller 29-4               | 29004 |  1532029 |  1427066 |  1163354 |   874390 |  1584332 |  1360211 |  1145326 |  1013490 |   788432 |   633882 |  1476259 |  1761088 |   633882 |      3.92109e+06 |  0.16166     |
| Mitchell 17-2             | 17002 |  4868855 |  5049451 |  4478609 |  4090629 |  5384735 |  4720999 |  4053730 |  3813393 |  3788406 |  3440459 |  4990763 |  4917925 |  3440459 |      1.90788e+07 |  0.180329    |
| Mobridge-Pollock 62-6     | 62006 |  1527616 |  1560066 |  1387594 |  1186594 |  1306268 |  1276624 |  1111208 |  1063842 |  1039851 |   914783 |  1478972 |  1836696 |   914783 |      4.71654e+06 |  0.193952    |
| Montrose 43-2             | 43002 |   860568 |   822943 |   753169 |   700298 |   733911 |   690552 |   614342 |   569802 |   536114 |   553591 |   683484 |   928894 |   536114 |      2.07403e+06 |  0.258489    |
| Mount Vernon 17-3         | 17003 |   900672 |   870410 |   772039 |   662086 |   789735 |   743675 |   654262 |   636066 |   578883 |   539568 |   688689 |   883791 |   539568 |      2.11268e+06 |  0.255395    |
| New Underwood 51-3        | 51003 |   455890 |   486513 |   464634 |   438495 |   496220 |   504492 |   519258 |   518003 |   487404 |   483404 |   576093 |   686146 |   438495 |      1.8732e+06  |  0.234088    |
| Newell 09-2               |  9002 |   681041 |   720754 |   421049 |   535343 |   649074 |   633616 |   642869 |   576932 |   565040 |   535029 |   683032 |   744914 |   421049 |      2.88995e+06 |  0.145694    |
| Northwestern Area 56-7    | 56007 |   900527 |   826344 |   674077 |   527418 |   822414 |   797445 |   646729 |   531635 |   443377 |   493892 |   870630 |   930994 |   443377 |      2.20369e+06 |  0.201198    |
| Oelrichs 23-3             | 23003 |    -6030 |      157 |   -77163 |    84978 |    27756 |    46051 |    49076 |    28099 |    56510 |     9970 |     9132 |     1658 |   -77163 |      2.19666e+06 | -0.0351274   |
| Oglala Lakota County 65-1 | 65001 |  -480964 | -1725541 | -2785336 | -3294559 | -2872531 | -3647966 | -4125350 | -4410396 | -5320031 | -6055420 | -6171625 |   477668 | -6171625 |      2.17284e+07 | -0.284035    |
| Oldham-Ramona 39-5        | 39005 |   850768 |   787308 |   701896 |   638410 |   786362 |   806860 |   734050 |   711773 |   690368 |   647394 |   981869 |   797757 |   638410 |      1.64065e+06 |  0.389121    |
| Parker 60-4               | 60004 |  1119691 |  1074435 |  1036176 |   951645 |  1099816 |  1075259 |  1005391 |   998712 |   912034 |   841514 |  1085665 |  1020759 |   841514 |      3.19564e+06 |  0.263332    |
| Parkston 33-3             | 33003 |  1315772 |  1320024 |  1145674 |  1084896 |  1252356 |  1222824 |  1079191 |  1033905 |   894687 |   773676 |  1136060 |  1505152 |   773676 |      4.14811e+06 |  0.186513    |
| Pierre 32-2               | 32002 |  5513921 |  5388168 |  4715900 |  4211915 |  5541751 |  5158350 |  5035436 |  4811768 |  4705159 |  4213722 |  5647670 |  5171166 |  4211915 |      1.75508e+07 |  0.239984    |
| Plankinton 01-1           |  1001 |   800482 |   812950 |   780224 |   774802 |   880376 |   995875 |   930903 |   926346 |   910221 |   858927 |  1152235 |  1065267 |   774802 |      2.9943e+06  |  0.258759    |
| Platte-Geddes 11-5        | 11005 |  1567285 |  1562312 |  1361773 |  1150994 |  1445756 |  1382175 |  1192659 |  1012666 |   889625 |   844526 |  1246436 |  1766306 |   844526 |      3.95495e+06 |  0.213536    |
| Rapid City Area 51-4      | 51004 | 14334913 | 12092916 | 11675906 |  8947012 | 19687764 | 18295976 | 14453729 | 12878565 | 10411556 |  8096814 | 19730650 | 14903718 |  8096814 |      9.45142e+07 |  0.0856677   |
| Redfield 56-4             | 56004 |  1207609 |   995441 |   831720 |   663734 |  1001104 |  1024392 |   866942 |   807562 |   647712 |   686928 |  1491248 |  1417208 |   647712 |      4.42838e+06 |  0.146264    |
| Rosholt 54-4              | 54004 |   530980 |   422375 |   414591 |   356649 |   432786 |   418286 |   332129 |   283022 |   258856 |   199044 |   415308 |   395574 |   199044 |      2.44569e+06 |  0.0813855   |
| Rutland 39-4              | 39004 |   252320 |   177582 |   133192 |    92935 |   305166 |   316079 |   267578 |   254448 |   256253 |   213458 |   494675 |   587559 |    92935 |      1.64459e+06 |  0.0565095   |
| Sanborn Central 55-5      | 55005 |   408260 |   348045 |   269857 |   184360 |   377886 |   339315 |   350984 |   299876 |   244101 |   218405 |   586684 |   587261 |   184360 |      2.05209e+06 |  0.0898402   |
| Scotland 04-3             |  4003 |   942618 |   928313 |   809144 |   687721 |   825530 |   750044 |   640584 |   610273 |   592313 |   534606 |   742997 |  1134641 |   534606 |      2.3023e+06  |  0.232205    |
| Selby Area 62-5           | 62005 |   922487 |   846480 |   691123 |   539163 |   802111 |   711519 |   671584 |   611318 |   524749 |   447160 |  1006896 |   928877 |   447160 |      2.0304e+06  |  0.220232    |
| Sioux Falls 49-5          | 49005 | 30848613 | 26452541 | 19027139 | 12477701 | 22333236 | 27543902 | 21222652 | 17323653 | 16198395 | 11078792 | 28577620 | 33354009 | 11078792 |      1.77781e+08 |  0.0623171   |
| Sioux Valley 05-5         |  5005 |  1621098 |  1571943 |  1463561 |   937482 |  1274532 |  1305242 |  1238841 |  1207176 |  1119259 |   948769 |  1919751 |  1929712 |   937482 |      4.40293e+06 |  0.212922    |
| Sisseton 54-2             | 54002 |   653360 |   960014 |   601250 |   405801 |   549259 |   296188 |   305037 |   135168 |    22228 |  -236632 |   155705 |  1347314 |  -236632 |      8.51953e+06 | -0.0277753   |
| Smee 15-3                 | 15003 |   199558 |   104539 |   -18449 |  -162310 |  -297172 |  -476650 |  -516814 |  -642600 |  -759527 |   424646 |   223503 |   166018 |  -759527 |      3.29222e+06 | -0.230703    |
| South Central 26-5        | 26005 |   287515 |   240160 |   171893 |    98977 |   132145 |    55068 |   -30934 |   -82246 |   -61461 |   -97866 |     8309 |   273608 |   -97866 |      1.39936e+06 | -0.0699361   |
| Spearfish 40-2            | 40002 |  4619918 |  4355587 |  3891165 |  3439098 |  5039543 |  4927929 |  4539381 |  4472822 |  4158153 |  3825599 |  5141971 |  5564194 |  3439098 |      1.61209e+07 |  0.213331    |
| Stanley County 57-1       | 57001 |   584503 |   527544 |   356970 |   183236 |   518374 |   436123 |   269147 |    88821 |   104233 |   211989 |   406111 |   689297 |    88821 |      3.69929e+06 |  0.0240103   |
| Summit 54-6               | 54006 |   386306 |   378709 |   275492 |   226649 |   277034 |   376057 |   326072 |   290155 |   262012 |   194464 |   301261 |   436058 |   194464 |      1.72139e+06 |  0.112969    |
| Tea Area 41-5             | 41005 |  1849821 |  1662581 |  1391026 |  1138863 |  1653331 |  1710576 |  1547489 |  1521749 |  1546427 |  1485943 |  2229649 |  2113228 |  1138863 |      1.14368e+07 |  0.099579    |
| Timber Lake 20-3          | 20003 |   270078 |   293893 |   194256 |   220838 |   277203 |   321353 |   332911 |   309260 |   284531 |   263549 |   423998 |   368492 |   194256 |      4.19664e+06 |  0.0462884   |
| Todd County 66-1          | 66001 |  2748738 |  3063178 |  2241968 |  1346089 |   672795 |  -105758 |   296421 |  1351358 |   925199 |   708379 |   -22836 |  3382638 |  -105758 |      2.32143e+07 | -0.00455573  |
| Tripp-Delmont 33-5        | 33005 |  1237605 |  1181179 |  1036711 |   922658 |  1217702 |  1154501 |  1024975 |   903088 |   804888 |   750605 |  1046111 |  1158110 |   750605 |      1.94122e+06 |  0.386667    |
| Tri-Valley 49-6           | 49006 |  2037015 |  1941119 |  1758238 |  1495866 |  1711261 |  1840896 |  1584599 |  1439620 |  1448154 |  1263200 |  1832169 |  1861218 |  1263200 |      6.66044e+06 |  0.189657    |
| Vermillion 13-1           | 13001 |  2454792 |  2371431 |  2104688 |  1728611 |  2752835 |  2710146 |  2429419 |  2315541 |  2154499 |  1962567 |  3070069 |  2561157 |  1728611 |      9.18842e+06 |  0.188129    |
| Viborg-Hurley 60-6        | 60006 |  1097412 |   992884 |   871056 |   790022 |  1006816 |   899116 |   820489 |   802845 |   686957 |   617043 |   916995 |   960867 |   617043 |      2.75468e+06 |  0.223998    |
| Wagner Community 11-4     | 11004 |  -429775 |  -602862 | -1041902 | -1359639 |  -179083 |  -515888 |  -805903 |  -608464 |  -895072 |  -205505 |   206744 |   130725 | -1359639 |      8.89956e+06 | -0.152776    |
| Wall 51-5                 | 51005 |   487293 |   469140 |   284454 |   189712 |   340958 |   340705 |   289496 |   206486 |   126486 |    49072 |   240786 |   493743 |    49072 |      2.60584e+06 |  0.0188316   |
| Warner 06-5               |  6005 |   571004 |   518798 |   441283 |   370971 |   501685 |   480534 |   449988 |   424129 |   395768 |   350031 |   465023 |   627045 |   350031 |      2.2997e+06  |  0.152207    |
| Watertown 14-4            | 14004 |  6798531 |  6544594 |  5396253 |  5098291 |  7143078 |  6770230 |  5897196 |  5410152 |  4923122 |  4243576 |  7227520 |  7651456 |  4243576 |      2.66713e+07 |  0.159106    |
| Waubay 18-3               | 18003 |   707643 |   662322 |   548457 |   474121 |   673138 |   617224 |   550639 |   509738 |   434147 |   368045 |   631679 |   695922 |   368045 |      1.94282e+06 |  0.189439    |
| Waverly 14-5              | 14005 |   474345 |   443954 |   315899 |   237547 |   373733 |   352012 |   269673 |   231460 |   231813 |   183670 |   358077 |   346568 |   183670 |      2.33355e+06 |  0.0787083   |
| Webster Area 18-5         | 18005 |  1394602 |  1334787 |  1082805 |   857175 |  1257032 |  1161491 |   962273 |   850753 |   687991 |   529304 |  1098594 |  1478759 |   529304 |      4.05712e+06 |  0.130463    |
| Wessington Springs 36-2   | 36002 |  1271153 |  1257213 |  1129081 |   967565 |  1227334 |  1158737 |  1065183 |   982547 |   891121 |   745546 |  1289480 |  1442654 |   745546 |      2.74177e+06 |  0.271921    |
| West Central 49-7         | 49007 |  1370879 |  1094868 |   862393 |   626306 |   908827 |  1142625 |   943024 |   935080 |   931356 |   963132 |  2058332 |  2083627 |   626306 |      9.35484e+06 |  0.0669499   |
| White Lake 01-3           |  1003 |   939898 |   874296 |   739265 |   664534 |   763775 |   718109 |   636587 |   571409 |   509214 |   474654 |   757585 |   965104 |   474654 |      1.39784e+06 |  0.339562    |
| White River 47-1          | 47001 |   237866 |    35373 |  -170413 |  -338941 |  -381924 |   -36589 |  -160918 |    -7757 |  -110112 |  -216940 |  -248752 |   258395 |  -381924 |      4.62987e+06 | -0.0824914   |
| Willow Lake 12-3          | 12003 |  1229359 |  1151211 |  1025540 |   904899 |  1134413 |  1089903 |   987772 |   934401 |   844467 |   767517 |   949170 |   810942 |   767517 |      2.55949e+06 |  0.299871    |
| Wilmot 54-7               | 54007 |   521433 |   511965 |   431357 |   363017 |   464396 |   457000 |   412661 |   220330 |   213990 |   165063 |   258651 |   552682 |   165063 |      1.946e+06   |  0.0848218   |
| Winner 59-2               | 59002 |  1217139 |  1250001 |  1028210 |   845365 |  1150378 |  1078774 |   957724 |   820993 |   726482 |   647363 |   886196 |  1091816 |   647363 |      5.40968e+06 |  0.119668    |
| Wolsey-Wessington 02-6    |  2006 |   876208 |   949747 |   846168 |   750748 |  1070150 |   994243 |   869340 |   786909 |   712430 |   694030 |   989819 |  1027533 |   694030 |      2.99696e+06 |  0.231578    |
| Woonsocket 55-4           | 55004 |   687435 |   699280 |   653097 |   582869 |   665479 |   645870 |   601581 |   591282 |   545906 |   472457 |   581459 |   745448 |   472457 |      1.80186e+06 |  0.262205    |
| Yankton 63-3              | 63003 |  5337157 |  5502265 |  4917817 |  4143126 |  5933255 |  5561300 |  5116318 |  4619622 |  4236998 |  3860758 |  5760080 |  5332925 |  3860758 |      1.86521e+07 |  0.206987    |



label: Q=O/P
labeled_formulas: Q=O/P
output: {"Arithmetic-Relationship": ["Q=O/P"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_548890___xlsx_235ae00e89508f9f2eea78f5dc29b5fb36c7da5a.xlsx___line_139