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 |  8143306 |  7995944 |  6941511 |  5653431 |  8433411 |  8342863 |  7475993 |  6785938 |  6467937 |  5582186 |  7631139 |  8682339 |  5582186 |      2.42008e+07 | 0.230662    |
| Agar-Blunt-Onida 58-3      | 58003 |  2040253 |  1961255 |  1685477 |  1500807 |  1931879 |  1847236 |  1736974 |  1794661 |  1755799 |  1638272 |  2170503 |  2092872 |  1500807 |      2.64399e+06 | 0.56763     |
| Alcester-Hudson 61-1       | 61001 |  1233082 |  1228185 |  1097082 |   970409 |  1270166 |  1312641 |  1213588 |  1168062 |  1134026 |  1113813 |  1436845 |  1412379 |   970409 |      2.22283e+06 | 0.436565    |
| Andes Central 11-1         | 11001 |     3659 |   155528 |   -23479 |  -184167 |   411212 |   327587 |   169929 |    85324 |   172316 |    59110 |   206466 |   412388 |        0 |      3.78466e+06 | 0           |
| Arlington 38-1             | 38001 |  1359897 |  1303746 |  1179352 |  1034786 |  1249411 |  1212022 |  1121390 |  1064366 |   998777 |   938442 |  1374835 |  1407435 |   938442 |      2.10826e+06 | 0.445126    |
| Armour 21-1                | 21001 |   874570 |   814354 |   800688 |   726586 |   967778 |   947332 |   893390 |   867690 |   818163 |   819667 |  1073009 |  1062110 |   726586 |      1.47181e+06 | 0.493668    |
| Avon 04-1                  |  4001 |   589854 |   556352 |   512481 |   445550 |   532958 |   535653 |   492729 |   485757 |   516998 |   498907 |   576917 |   714431 |   445550 |      1.70337e+06 | 0.26157     |
| Baltic 49-1                | 49001 |  1135693 |  1082057 |  1022874 |   877438 |  1015090 |  1050807 |   977323 |   964107 |   982245 |   916185 |  1035991 |  1138658 |   877438 |      2.78661e+06 | 0.314876    |
| Belle Fourche 09-1         |  9001 |  2655614 |  2612881 |  2203788 |  2030766 |  2690405 |  2707534 |  2344879 |  2251738 |  2185421 |  2015020 |  2687407 |  2785878 |  2015020 |      8.4513e+06  | 0.238427    |
| Bennett County 03-1        |  3001 |   569739 |   484491 |   430240 |   335351 |   457160 |   378576 |   328897 |   278358 |   184863 |   115958 |   199658 |    90637 |    90637 |      4.58216e+06 | 0.0197804   |
| Beresford 61-2             | 61002 |  1408551 |  1296948 |  1182277 |  1027696 |  1398122 |  1339454 |  1216233 |  1177172 |  1084963 |  1089756 |  1427585 |  1405149 |  1027696 |      3.84799e+06 | 0.267074    |
| Big Stone City 25-1        | 25001 |   216154 |   185011 |   154580 |   174127 |   215834 |   242906 |   206637 |   108951 |   139168 |    91917 |   215095 |   248625 |    91917 |      1.2153e+06  | 0.075633    |
| Bison 52-1                 | 52001 |   852445 |   982541 |   878306 |   792715 |   972671 |   928471 |   938611 |   866396 |   860515 |   818511 |   943664 |   875773 |   792715 |      1.52691e+06 | 0.519164    |
| Bon Homme 04-2             |  4002 |   174438 |   151616 |    53890 |    77008 |   112030 |   108635 |    41588 |    71891 |     9028 |    68681 |   196167 |    93469 |     9028 |      3.60083e+06 | 0.0025072   |
| Bowdle 22-1                | 22001 |   700629 |   672980 |   614591 |   548258 |   734075 |   725429 |   645222 |   649784 |   568494 |   526462 |   690566 |   738760 |   526462 |      1.19654e+06 | 0.439987    |
| Brandon Valley 49-2        | 49002 |  6664942 |  5922775 |  5014568 |  4303195 |  5365065 |  5686650 |  5338861 |  4990540 |  4776571 |  4101296 |  5969324 |  6489630 |  4101296 |      2.06012e+07 | 0.19908     |
| Bridgewater-Emery 30-3     | 30003 |  1710821 |  1689514 |  1585829 |  1463534 |  1605199 |  1590802 |  1484155 |  1398809 |  1304864 |  1240829 |  1437402 |  1748985 |  1240829 |      2.37903e+06 | 0.52157     |
| Britton-Hecla 45-4         | 45004 |  1077858 |   993474 |   844594 |   693631 |  1136555 |  1049964 |   886430 |   817499 |   696571 |   610301 |  1063133 |  1242593 |   610301 |      2.96921e+06 | 0.205543    |
| Brookings 05-1             |  5001 |  6021278 |  5181538 |  4301357 |  3342082 |  6174343 |  6105242 |  5371330 |  5181441 |  4417033 |  3518548 |  6776363 |  6338413 |  3342082 |      1.88858e+07 | 0.176963    |
| Burke 26-2                 | 26002 |   538231 |   509767 |   464431 |   359870 |   595719 |   570850 |   530358 |   511677 |   432178 |   426640 |   564106 |   585284 |   359870 |      1.93173e+06 | 0.186294    |
| Canistota 43-1             | 43001 |  1049008 |  1019377 |   977135 |   936464 |  1119928 |  1085126 |  1027375 |   993935 |   968014 |   914687 |  1056082 |  1147320 |   914687 |      1.63452e+06 | 0.559606    |
| Canton 41-1                | 41001 |  3117374 |  2976268 |  2737240 |  2603036 |  3013085 |  3063916 |  2881638 |  2836198 |  2731988 |  2600412 |  3158627 |  3090526 |  2600412 |      5.03234e+06 | 0.51674     |
| Castlewood 28-1            | 28001 |   684587 |   676270 |   629841 |   560948 |   741333 |   802007 |   776903 |   751747 |   704084 |   681391 |   833749 |   829532 |   560948 |      1.87563e+06 | 0.299071    |
| Centerville 60-1           | 60001 |   684987 |   642039 |   580387 |   507186 |   659774 |   672438 |   604606 |   602811 |   548724 |   533624 |   650612 |   720285 |   507186 |      1.60066e+06 | 0.31686     |
| Chamberlain 07-1           |  7001 |   654296 |   724633 |   574840 |   354814 |   735053 |   595443 |   387733 |   275991 |   115368 |   -47483 |   303972 |     2404 |        0 |      6.84816e+06 | 0           |
| Chester Area 39-1          | 39001 |  1152394 |  1067196 |   968143 |   855688 |  1132218 |  1161973 |  1088514 |  1084456 |  1036048 |   956082 |  1203331 |  1234999 |   855688 |      3.28251e+06 | 0.260681    |
| Clark 12-2                 | 12002 |   546028 |   488409 |   313181 |    97381 |   654550 |   618886 |   487405 |   459621 |   272481 |   269703 |   789709 |   768208 |    97381 |      2.57654e+06 | 0.0377952   |
| Colman-Egan 50-5           | 50005 |   403486 |   363897 |   301731 |   246816 |   373975 |   356208 |   320860 |   316438 |   253103 |    62270 |   409158 |   454978 |    62270 |      1.59788e+06 | 0.0389705   |
| Colome Consolidated 59-3   | 59003 |  1278326 |  1248257 |  1109942 |  1123189 |  1189317 |  1183837 |  1134423 |  1153466 |  1126466 |  1132562 |  1218563 |  1068112 |  1068112 |      1.84853e+06 | 0.577816    |
| Corsica 21-2               | 21002 |   343716 |   337979 |   278652 |   214148 |   362824 |   339590 |   278422 |   245621 |   224916 |   196230 |   288212 |  1088345 |   196230 |      1.28723e+06 | 0.152443    |
| Custer 16-1                | 16001 |  1546541 |  1488547 |   987982 |   714005 |  1390637 |  1435512 |  1046813 |   638234 |   234717 |   427365 |  1282010 |  2381309 |   234717 |      6.17434e+06 | 0.0380149   |
| Dakota Valley 61-8         | 61008 |  1584448 |  1214442 |   724567 |   806805 |  1975970 |  1551690 |  1689590 |  1429397 |  1121101 |   861439 |  2147975 |  2130145 |   724567 |      7.34369e+06 | 0.0986653   |
| De Smet 38-2               | 38002 |  1017235 |   949438 |   836719 |   740323 |   966597 |   929187 |   831906 |   756664 |   685137 |   626307 |   905613 |   978893 |   626307 |      2.32802e+06 | 0.269029    |
| Dell Rapids 49-3           | 49003 |  1414640 |  1416895 |  1248979 |  1033162 |  1424054 |  1502819 |  1334552 |  1235285 |  1261573 |  1149407 |  1439171 |  1570843 |  1033162 |      5.11844e+06 | 0.201851    |
| Deubrook Area 05-6         |  5006 |   796052 |   757445 |   601836 |   362928 |   605327 |   597532 |   469036 |   433627 |   314800 |   218673 |   958023 |   999327 |   218673 |      2.70305e+06 | 0.0808985   |
| Deuel 19-4                 | 19004 |  1738999 |  1761005 |  1631334 |  1511986 |  1837993 |  1818446 |  1677195 |  1646112 |  1554635 |  1489760 |  1791788 |  1956138 |  1489760 |      2.95158e+06 | 0.504733    |
| Doland 56-2                | 56002 |   772641 |   697848 |   660221 |   582199 |   833445 |   823218 |   815179 |   750141 |   697209 |   666451 |   863188 |  1169230 |   582199 |      1.39364e+06 | 0.417754    |
| Douglas 51-1               | 51001 |   163072 |  -218495 |  -739112 | -1266548 |  -818344 | -1101140 | -1811464 | -2126298 | -2878399 | -3147135 | -3118144 |  1024027 |        0 |      1.94122e+07 | 0           |
| Dupree 64-2                | 64002 |   399417 |   199518 |   214333 |    48585 |   224312 |   166066 |    56785 |   -53780 |   127272 |    65102 |    35944 |   507076 |        0 |      3.95986e+06 | 0           |
| Eagle Butte 20-1           | 20001 |   300849 |   354575 |   380375 |  -135639 |    72526 |    52497 |  -206483 |   223573 |   236262 |   -35226 |   -62693 |   223172 |        0 |      5.11461e+06 | 0           |
| Edgemont 23-1              | 23001 |  1225064 |  1173038 |  1070073 |   975183 |  1267383 |  1201803 |  1202085 |  1117903 |  1024141 |   970857 |  1251694 |  1290213 |   970857 |      1.68947e+06 | 0.574653    |
| Edmunds Central 22-5       | 22005 |   662657 |   608366 |   486349 |   393369 |   562887 |   503262 |   521343 |   440843 |   404346 |   364991 |   685069 |   738840 |   364991 |      1.28507e+06 | 0.284025    |
| Elk Mountain 16-2          | 16002 |   171330 |   154266 |   136253 |   109678 |    91456 |    78605 |    55718 |    38914 |    23930 |     7086 |   -13163 |   207887 |        0 | 249659           | 0           |
| Elk Point-Jefferson 61-7   | 61007 |  1457110 |  1365338 |  1221355 |  1090897 |  1477974 |  1451616 |  1306687 |  1262256 |  1269593 |  1189198 |  1658958 |  1589019 |  1090897 |      3.93569e+06 | 0.277181    |
| Elkton 05-3                |  5003 |   630661 |   516800 |   363292 |   173304 |   339306 |   369924 |   305132 |   212455 |   152797 |    31159 |   241354 |   599097 |    31159 |      2.36163e+06 | 0.0131939   |
| Estelline 28-2             | 28002 |  1356388 |  1298447 |  1193193 |  1071547 |  1333362 |  1306401 |  1202719 |  1152631 |  1053741 |   982616 |  1176512 |  1183748 |   982616 |      1.94198e+06 | 0.505986    |
| Ethan 17-1                 | 17001 |   839824 |   802808 |   773130 |   735020 |   810664 |   817691 |   796157 |   765390 |   751283 |   761997 |   852192 |   884883 |   735020 |      1.50922e+06 | 0.487019    |
| Eureka 44-1                | 44001 |  1735636 |  1695636 |  1581841 |  1507591 |  1702053 |  1652486 |  1691331 |  1609925 |  1566002 |  1493429 |  1717391 |  1669572 |  1493429 |      1.51549e+06 | 0.985444    |
| Faith 46-2                 | 46002 |   533955 |   542972 |   468787 |   435745 |   510518 |   511822 |   560781 |   541291 |   583523 |   568128 |   604596 |   652969 |   435745 |      1.38311e+06 | 0.315048    |
| Faulkton Area Schools 24-4 | 24004 |   540851 |   568464 |   431588 |   294570 |   602839 |   564710 |   442201 |   363058 |   260177 |   164954 |   699607 |   759545 |   164954 |      2.05349e+06 | 0.0803287   |
| Flandreau 50-3             | 50003 |  1160793 |  1133428 |   974172 |   804922 |  1063170 |  1055775 |   979796 |   965365 |   870184 |   818604 |  1385606 |  1281543 |   804922 |      3.82893e+06 | 0.210221    |
| Florence 14-1              | 14001 |   585982 |   534524 |   457244 |   409151 |   522917 |   527122 |   483635 |   487643 |   446836 |   421250 |   508025 |   634863 |   409151 |      1.50992e+06 | 0.270976    |
| Frederick Area 06-2        |  6002 |   291962 |   265466 |   199145 |   156033 |   288862 |   290484 |   247613 |   191031 |   179885 |   161716 |   311784 |   307557 |   156033 |      1.37274e+06 | 0.113665    |
| Freeman 33-1               | 33001 |   800404 |   769198 |   628004 |   512633 |   817907 |   790478 |   712582 |   664801 |   569872 |   503744 |   826469 |   895342 |   503744 |      2.6203e+06  | 0.192247    |
| Garretson 49-4             | 49004 |  1291363 |  1246796 |  1135158 |   983806 |  1134548 |  1128840 |  1029213 |   959729 |   903828 |   812118 |  1001871 |  1209838 |   812118 |      3.1633e+06  | 0.256731    |
| Gayville-Volin 63-1        | 63001 |   938391 |   903427 |   870847 |   842305 |   930511 |   923855 |   899556 |   884801 |   876409 |   875544 |   947323 |   969510 |   842305 |      1.73111e+06 | 0.48657     |
| Gettysburg 53-1            | 53001 |   867080 |   862334 |   811366 |   739340 |   885518 |   847239 |   765883 |   705954 |   686703 |   655665 |   800338 |   880473 |   655665 |      1.88088e+06 | 0.348595    |
| Grant-Deuel 25-3           | 25003 |   414327 |   347832 |   304247 |   220661 |   376241 |   391532 |   308998 |   257129 |   226655 |   444659 |   398169 |   509718 |   220661 | 988225           | 0.22329     |
| Gregory 26-4               | 26004 |   728858 |   820223 |   715817 |   619199 |   728878 |   793584 |   690209 |   668031 |   574473 |   683365 |   674792 |   671350 |   574473 |      2.71361e+06 | 0.211701    |
| Groton Area 06-6           |  6006 |  1959260 |  1953721 |  1657875 |  1363278 |  1957013 |  2047072 |  1734960 |  1475298 |  1279688 |  1045119 |  1759350 |  1599596 |  1045119 |      4.2366e+06  | 0.246688    |
| Haakon 27-1                | 27001 |  1258703 |  1368143 |  1289042 |  1188849 |  1296827 |  1396156 |  1341030 |  1255888 |  1232989 |  1234543 |  1287515 |  1498691 |  1188849 |      1.9975e+06  | 0.595169    |
| Hamlin 28-3                | 28003 |  2245227 |  2157002 |  1994156 |  1828236 |  2210202 |  2220575 |  2041060 |  2067000 |  1951673 |  1913911 |  2331241 |  2364747 |  1828236 |      4.08375e+06 | 0.447685    |
| Hanson 30-1                | 30001 |   794093 |   759917 |   712604 |   641722 |   842844 |   823410 |   788746 |   762815 |   726874 |   698294 |   868141 |   995942 |   641722 |      2.36801e+06 | 0.270997    |
| Harding County 31-1        | 31001 |  1146041 |  1111988 |   914519 |   912166 |  1002385 |  1089897 |  1047520 |   917896 |   858168 |   939383 |  1193835 |  1587381 |   858168 |      2.41058e+06 | 0.356001    |
| Harrisburg 41-2            | 41002 |  4704490 |  3911277 |  2818995 |  1915601 |  4222355 |  4738116 |  3872351 |  3647553 |  3125740 |  2591929 |  5228014 |  5871894 |  1915601 |      2.00083e+07 | 0.0957403   |
| Henry 14-2                 | 14002 |   435529 |   412868 |   373517 |   345348 |   396298 |   390600 |   378620 |   419727 |   376134 |   367069 |   422710 |   510341 |   345348 |      1.1491e+06  | 0.300537    |
| Herreid 10-1               | 10001 |   157764 |   109018 |    56137 |     -821 |   182852 |   220218 |   170764 |   109737 |    82424 |   125810 |   226146 |   208765 |        0 |      1.14263e+06 | 0           |
| Highmore-Harrold 34-2      | 34002 |   300352 |   280356 |   143790 |    14432 |   303569 |   292531 |   209062 |   158203 |    98495 |    22228 |   349607 |   325225 |    14432 |      2.00441e+06 | 0.00720013  |
| Hill City 51-2             | 51002 |   558469 |   502787 |   253506 |   -23971 |   579258 |   439265 |   313112 |   458283 |   419836 |   195843 |   917598 |  1278317 |        0 |      4.29964e+06 | 0           |
| Hitchcock-Tulare 56-6      | 56006 |   995931 |   918243 |   809383 |   709742 |   999715 |   950625 |    81545 |   732566 |   658069 |   602747 |   839068 |   951277 |    81545 |      1.92431e+06 | 0.0423763   |
| Hot Springs 23-2           | 23002 |   482109 |   615837 |   380783 |   219753 |   650509 |   540902 |   353699 |   175548 |   117117 |     3938 |   600035 |   567866 |     3938 |      5.05186e+06 | 0.000779515 |
| Hoven 53-2                 | 53002 |   927537 |   892570 |   810779 |   662008 |   953235 |   903253 |   912287 |   877252 |   883240 |   842489 |  1174952 |  1170586 |   662008 |      1.37923e+06 | 0.479983    |
| Howard 48-3                | 48003 |  1136497 |   998033 |   852880 |   707448 |  1061761 |   975440 |   824957 |   708425 |   619698 |   550233 |   790395 |   932055 |   550233 |      2.58286e+06 | 0.213032    |
| Huron 02-2                 |  2002 |  3593113 |  3549190 |  3009720 |  2399576 |  3789754 |  4094508 |  3688541 |  3417712 |  3095216 |  2816521 |  3549611 |  3782949 |  2399576 |      1.56379e+07 | 0.153447    |
| Ipswich Public 22-6        | 22006 |  1315731 |  1227942 |  1040364 |   874641 |  1281941 |  1279106 |  1110612 |  1008420 |   891210 |   780502 |  1231455 |  1251298 |   780502 |      2.60464e+06 | 0.299658    |
| Irene-Wakonda 13-3         | 13003 |   820595 |   753095 |   667471 |   580838 |   839502 |   846553 |   756308 |   778076 |   733501 |   691125 |   953907 |   962104 |   580838 |      2.01851e+06 | 0.287756    |
| Iroquois 02-3              |  2003 |  2034389 |  1983538 |  1858652 |  1742796 |  2200798 |  2216638 |  2096115 |  1970857 |  1893742 |  1872215 |  2151712 |  2246279 |  1742796 |      1.96282e+06 | 0.887903    |
| Jones County 37-3          | 37003 |   605607 |   560759 |   485082 |   424410 |   556164 |   510569 |   561335 |   545562 |   475864 |   432527 |   536888 |   608855 |   424410 |      1.58884e+06 | 0.267119    |
| Kadoka Area 35-2           | 35002 |   646515 |   779969 |   646860 |   544844 |   630105 |   677015 |   637556 |   601319 |   537542 |   496050 |   538005 |   740628 |   496050 |      3.7048e+06  | 0.133894    |
| Kimball 07-2               |  7002 |   867283 |   869370 |   781577 |   678941 |   829124 |   811428 |   711404 |   635670 |   559060 |   560258 |   736044 |   816234 |   559060 |      2.15e+06    | 0.260029    |
| Lake Preston 38-3          | 38003 |   587481 |   573112 |   482953 |   406655 |   582178 |   512190 |   412856 |   337732 |   314198 |   270906 |   430898 |   349848 |   270906 |      1.65938e+06 | 0.163257    |
| Langford Area 45-5         | 45005 |   712863 |   626900 |   574036 |   485467 |   708223 |   685767 |   596951 |   573381 |   509859 |   477967 |   678618 |   774318 |   477967 |      1.51089e+06 | 0.316347    |
| Lead-Deadwood 40-1         | 40001 |  5033426 |  4749987 |  4194301 |  3835511 |  5015600 |  4965158 |  4591947 |  4281622 |  4266410 |  4127313 |  5774163 |  5708062 |  3835511 |      7.19926e+06 | 0.532765    |
| Lemmon 52-4                | 52004 |     9750 |    47769 |   -59640 |  -167886 |    58917 |    41553 |    -5616 |   -90515 |   -94243 |  -139523 |   172811 |   205725 |        0 |      2.15809e+06 | 0           |
| Lennox 41-4                | 41004 |  1697041 |  1665782 |  1463312 |  1281876 |  1684233 |  1659991 |  1431721 |  1355644 |  1220072 |  1103378 |  1614983 |  1636354 |  1103378 |      5.76959e+06 | 0.19124     |
| Leola 44-2                 | 44002 |   250501 |   284373 |   194079 |    98657 |   335653 |   285179 |   318733 |   256437 |   174075 |   129753 |   483717 |   492836 |    98657 |      1.65984e+06 | 0.0594377   |
| Lyman 42-1                 | 42001 |  1323448 |  1486156 |  1300819 |  1114068 |  1295895 |  1161674 |  1152031 |  1013492 |  1185290 |  1039513 |  1381729 |  1153595 |  1013492 |      3.71068e+06 | 0.273128    |
| Madison Central 39-2       | 39002 |  2902014 |  2627742 |  2285793 |  1982139 |  2771665 |  2718483 |  2498379 |  2280985 |  2101953 |  1901949 |  2730519 |  2971644 |  1901949 |      6.75358e+06 | 0.281621    |
| Marion 60-3                | 60003 |  1212444 |  1192876 |  1122960 |  1037219 |  1126835 |  1129816 |  1052341 |  1001908 |   913317 |   861022 |   973945 |   946154 |   861022 |      1.65418e+06 | 0.520514    |
| McCook Central 43-7        | 43007 |  1527953 |  1499389 |  1417885 |  1280387 |  1561370 |  1522787 |  1406996 |  1335892 |  1233525 |  1188497 |  1484979 |  1427195 |  1188497 |      2.80659e+06 | 0.423467    |
| McIntosh 15-1              | 15001 |   -48424 |   248746 |   106524 |   288025 |   277121 |   193817 |    54116 |   192926 |    11419 |   204848 |   173757 |   162209 |        0 |      2.49011e+06 | 0           |
| McLaughlin 15-2            | 15002 |    78605 |   -43560 |  -425161 |  -856802 |  -937174 | -1381382 | -1480254 | -1657872 | -1828312 | -2024514 | -2302677 |   283843 |        0 |      6.24954e+06 | 0           |
| Meade 46-1                 | 46001 |  7229538 |  6915406 |  6336096 |  5813196 |  7327496 |  7543690 |  6730111 |  6399055 |  6076371 |  5628878 |  7286458 |  7673058 |  5628878 |      1.58751e+07 | 0.354574    |
| Menno 33-2                 | 33002 |  1921111 |  1886799 |  1770621 |  1670406 |  1878910 |  1848344 |  1774771 |  1740626 |  1681053 |  1655042 |  1827327 |  2152029 |  1655042 |      2.15468e+06 | 0.768117    |
| Milbank 25-4               | 25004 |  2008693 |  1864747 |  1592269 |  1518251 |  1721829 |  2128284 |  1948949 |  1630844 |  1508698 |  1347064 |  1827124 |  2189372 |  1347064 |      5.29697e+06 | 0.254308    |
| Miller 29-4                | 29004 |  1060196 |   941263 |   730112 |   556602 |  1053425 |  1010243 |   851647 |   723577 |   630232 |   517192 |  1089721 |  1103976 |   517192 |      2.8594e+06  | 0.180874    |
| Mitchell 17-2              | 17002 |  5173982 |  5179194 |  4533866 |  3740184 |  5504008 |  5185795 |  4599035 |  4526083 |  4024299 |  3500207 |  5417366 |  5105667 |  3500207 |      1.62885e+07 | 0.214888    |
| Mobridge-Pollock 62-6      | 62006 |  1672626 |  1676971 |  1700868 |  1571313 |  1895416 |  1968248 |  1858209 |  1869879 |  1758982 |  1800885 |  1984421 |  2297888 |  1571313 |      4.26463e+06 | 0.368452    |
| Montrose 43-2              | 43002 |   294096 |   284927 |   228782 |   171127 |   260868 |   245063 |   197922 |   240491 |   207432 |   160770 |   246298 |   279769 |   160770 |      1.50958e+06 | 0.1065      |
| Mount Vernon 17-3          | 17003 |   608950 |   547774 |   483346 |   266964 |   539492 |   501778 |   411004 |   351441 |   286513 |   241806 |   474390 |   638264 |   241806 |      1.68266e+06 | 0.143705    |
| New Underwood 51-3         | 51003 |   666593 |   621512 |   616831 |   589096 |   551131 |   664341 |   621764 |   621237 |   591407 |   582931 |   644253 |   665669 |   551131 |      1.80273e+06 | 0.305721    |
| Newell 09-2                |  9002 |  1281367 |  1455267 |  1384113 |  1317776 |  1490579 |  1473489 |  1415143 |  1360140 |  1360620 |  1237106 |  1382779 |  1400807 |  1237106 |      2.69694e+06 | 0.458708    |
| Northwestern Area 56-7     | 56007 |  1614636 |  1530842 |  1446411 |  1355521 |  1622176 |  1576686 |  1448513 |  1388332 |  1340167 |  1284929 |  1553334 |  1633001 |  1284929 |      1.76187e+06 | 0.729298    |
| Oelrichs 23-3              | 23003 |   247223 |   127759 |   111123 |   -94827 |  -227891 |  -389953 |  -585995 |  -680172 |  -855296 |  -366879 |  -602247 |   217506 |        0 |      2.08684e+06 | 0           |
| Oldham-Ramona 39-5         | 39005 |   668733 |   632268 |   569363 |   507400 |   686828 |   683464 |   625353 |   607703 |   578574 |   525253 |   702699 |   742137 |   507400 |      1.09565e+06 | 0.463102    |
| Parker 60-4                | 60004 |   794106 |   727356 |   695113 |   595691 |   818739 |   807834 |   721594 |   701324 |   642346 |   585747 |   835464 |   993024 |   585747 |      2.29543e+06 | 0.25518     |
| Parkston 33-3              | 33003 |  1595621 |  1545403 |  1511378 |  1382761 |  1549571 |  1483281 |  1343949 |  1282035 |  1267064 |  1215125 |  1429856 |  1612215 |  1215125 |      3.70893e+06 | 0.327621    |
| Pierre 32-2                | 32002 |  5093386 |  5038326 |  4450608 |  3902507 |  5399881 |  4996085 |  4634770 |  4313489 |  4396645 |  4002979 |  5467318 |  4927530 |  3902507 |      1.53779e+07 | 0.253775    |
| Plankinton 01-1            |  1001 |  1038341 |   960778 |   899276 |   808807 |   952377 |   935065 |   847710 |   776917 |   752922 |   697274 |   784804 |   838472 |   697274 |      2.84269e+06 | 0.245287    |
| Platte-Geddes 11-5         | 11005 |  2138185 |  2101190 |  1926181 |  1753088 |  2041600 |  2047336 |  1883134 |  1765934 |  1728830 |  1642516 |  1950665 |  2118321 |  1642516 |      3.12137e+06 | 0.526217    |
| Rapid City Area 51-4       | 51004 | 16000687 | 18288140 | 14795230 | 10316167 | 20270204 | 17947009 | 14293378 | 11950433 |  8959446 |  5926790 | 16833068 | 11798519 |  5926790 |      8.1456e+07  | 0.0727607   |
| Redfield 56-4              | 56004 |  2022128 |  1933037 |  1724609 |  1623804 |  2027065 |  2053172 |  1938402 |  1836657 |  1778686 |  1732297 |  2186736 |  2199243 |  1623804 |      4.0037e+06  | 0.405576    |
| Rosholt 54-4               | 54004 |  1093614 |  1024554 |  1021000 |   953969 |  1038475 |   916032 |   845621 |   740978 |   766940 |   701218 |   799702 |  1140116 |   701218 |      1.74917e+06 | 0.400886    |
| Rutland 39-4               | 39004 |   112530 |    76885 |    17731 |   -53279 |    37374 |    37402 |    25541 |   -16902 |   -47195 |   -93511 |    16119 |    31438 |        0 |      1.3505e+06  | 0           |
| Sanborn Central 55-5       | 55005 |   774362 |   716774 |   621697 |   552447 |   777891 |   758060 |   684384 |   615304 |   538157 |   499426 |   800448 |   781568 |   499426 |      1.64341e+06 | 0.303896    |
| Scotland 04-3              |  4003 |  2335072 |  2316059 |  2233383 |  2155670 |  2292841 |  2298339 |  2224658 |  2186384 |  2143128 |  2116083 |  2272639 |  2277947 |  2116083 |      1.92364e+06 | 1.10004     |
| Selby Area 62-5            | 62005 |  2017943 |  1947976 |  1823792 |  1680433 |  1933364 |  1824011 |  1816925 |  1714154 |  1611863 |  1516648 |  1838422 |  1820752 |  1516648 |      1.76018e+06 | 0.861645    |
| Shannon County 65-1        | 65001 |   305015 |    72107 |     4609 |  -433103 |  -911861 | -1326113 | -1654113 | -1733321 | -2129330 | -2498561 | -3167136 |      556 |        0 |      1.658e+07   | 0           |
| Sioux Falls 49-5           | 49005 | 32438337 | 30938567 | 24327939 | 17662440 | 33590951 | 35229645 | 29435274 | 24665397 | 21702506 | 15981985 | 33443218 | 30607936 | 15981985 |      1.40864e+08 | 0.113457    |
| Sioux Valley 05-5          |  5005 |  2726519 |  2643493 |  2477072 |  2288193 |  2743201 |  2755337 |  2594248 |  2595228 |  2476922 |  2357658 |  2724051 |  2712053 |  2288193 |      4.03939e+06 | 0.56647     |
| Sisseton 54-2              | 54002 |  1667789 |  1801370 |  1288082 |   792731 |  1166520 |  1103054 |   813231 |  2485431 |  2908002 |  1983603 |  2212500 |  2188254 |   792731 |      8.23119e+06 | 0.0963082   |
| Smee 15-3                  | 15003 |  -115241 |     4484 |  -147268 |  -249232 |  -326258 |  -342392 |  -453124 |  -462881 |  -571088 |  -582778 |  -675635 |   291117 |        0 |      2.77565e+06 | 0           |
| South Central 26-5         | 26005 |   384021 |   342067 |   259270 |   185909 |   238246 |   185291 |    86917 |   106437 |   128411 |   146353 |   291758 |   367268 |    86917 |      1.5889e+06  | 0.0547026   |
| Spearfish 40-2             | 40002 |  4322760 |  4185797 |  3577897 |  3117004 |  4864278 |  4655941 |  3992326 |  3563037 |  3355989 |  2892933 |  4781002 |  4320511 |  2892933 |      1.25936e+07 | 0.229714    |
| Stanley County 57-1        | 57001 |   480500 |   361531 |   149845 |   -37017 |   340312 |   267885 |   103408 |    11457 |    77599 |   -42913 |   563101 |   650203 |        0 |      3.21278e+06 | 0           |
| Stickney 01-2              |  1002 |   205829 |   246888 |   222231 |   168226 |   369234 |   338758 |   242984 |   206220 |   178869 |   154518 |   393260 |   895275 |   154518 |      1.17322e+06 | 0.131704    |
| Summit 54-6                | 54006 |   371162 |   374113 |   315972 |    27515 |   351537 |   367397 |   334163 |   277865 |   234963 |   241538 |   291594 |   322611 |    27515 |      1.30866e+06 | 0.0210253   |
| Tea Area 41-5              | 41005 |  1921797 |  1790734 |  1617652 |  1390085 |  1084794 |  1508716 |  1655353 |  1470910 |  1578503 |  1464267 |  1468437 |  2001643 |  1084794 |      7.98611e+06 | 0.135835    |
| Timber Lake 20-3           | 20003 |   303861 |   205260 |   162916 |   223692 |   237894 |   219285 |   214272 |   216980 |   224419 |   200076 |   376927 |   386250 |   162916 |      3.50658e+06 | 0.04646     |
| Todd County 66-1           | 66001 |   571396 |  1752218 |   749031 |  -129472 |  -248088 |  -227775 |   237813 |   350655 |  -142612 |   132823 |   -30238 |  1239145 |        0 |      2.08296e+07 | 0           |
| Tripp-Delmont 33-5         | 33005 |  1077961 |  1043065 |   946177 |   857939 |  1072467 |  1024657 |   931958 |   903086 |   844105 |   986294 |  1165579 |  1190991 |   844105 |      1.6505e+06  | 0.511424    |
| Tri-Valley 49-6            | 49006 |  2205541 |  2088465 |  1836889 |  1487388 |  2041604 |  2144469 |  1921801 |  1833813 |  1842872 |  1666386 |  2297734 |  2466619 |  1487388 |      5.40075e+06 | 0.275404    |
| Vermillion 13-1            | 13001 |  2218968 |  2158954 |  1839947 |  1466617 |  2643065 |  2559380 |  2260550 |  2127913 |  1840039 |  1600646 |  2704046 |  2334063 |  1466617 |      8.33686e+06 | 0.17592     |
| Viborg-Hurley 60-6         | 60006 |   911793 |   849381 |   819762 |   764130 |   953156 |   934897 |   838347 |   832655 |   788400 |   800512 |  1013857 |  1068151 |   764130 |      2.0508e+06  | 0.3726      |
| Wagner Community 11-4      | 11004 |   810440 |   514236 |   475147 |   202212 |   355450 |   167877 |   -72432 |   697942 |   969345 |   872474 |   949896 |  1932158 |        0 |      6.52982e+06 | 0           |
| Wall 51-5                  | 51005 |   465332 |   444213 |   347685 |   218947 |   450309 |   405141 |   331924 |  2659556 |   200829 |   130857 |   255859 |   794223 |   130857 |      2.339e+06   | 0.0559457   |
| Warner 06-5                |  6005 |   774681 |   739571 |   685476 |   625217 |   752527 |   726810 |   672193 |   636975 |   616332 |   600524 |   745922 |   730905 |   600524 |      1.97129e+06 | 0.304635    |
| Watertown 14-4             | 14004 |  6487687 |  6111293 |  5120596 |  4052587 |  6830879 |  6442023 |  5546384 |  5374715 |  4507646 |  4043853 |  7243491 |  6643262 |  4043853 |      2.27974e+07 | 0.177382    |
| Waubay 18-3                | 18003 |   106664 |    44363 |   -44430 |   -81959 |   -40255 |  -102929 |  -143656 |  -218402 |  -256086 |  -259851 |   -71070 |   241892 |        0 |      1.64908e+06 | 0           |
| Waverly 14-5               | 14005 |  1030510 |   984034 |   900274 |   829888 |  1006772 |  1000028 |   921633 |   930206 |   892395 |   844003 |  1036972 |   987763 |   829888 |      1.76885e+06 | 0.469167    |
| Webster Area 18-5          | 18005 |  1968564 |  1978635 |  1839980 |  1683873 |  2021333 |  1982788 |  1810539 |  1669425 |  1585544 |  1509207 |  1961777 |  2029854 |  1509207 |      3.23681e+06 | 0.466264    |
| Wessington Springs 36-2    | 36002 |   687099 |   691022 |   559167 |   421466 |  1327532 |   844043 |   769140 |   695051 |   642286 |   595098 |  1048639 |  1103935 |   421466 |      2.16646e+06 | 0.194542    |
| West Central 49-7          | 49007 |  2924621 |  2208161 |  1904030 |  1502583 |  2388737 |  2308666 |  2124964 |  2020920 |  2088209 |  1917797 |  2412381 |  2471292 |  1502583 |      8.23759e+06 | 0.182406    |
| White Lake 01-3            |  1003 |   669720 |   618339 |   537450 |   468199 |   613173 |   585774 |   523561 |   474082 |   457137 |   422192 |   712476 |   721407 |   422192 |      1.16646e+06 | 0.361943    |
| White River 47-1           | 47001 |   214637 |   108636 |   -56637 |  -344172 |  -416872 |    15920 |   -46702 |   111116 |  -231265 |  -332234 |  -451230 |   248219 |        0 |      4.29896e+06 | 0           |
| Willow Lake 12-3           | 12003 |  1631733 |  1563378 |  1459784 |  1387765 |  1620505 |  1557204 |  1463819 |  1389732 |  1306752 |  1226572 |  1357066 |  1354806 |  1226572 |      1.94723e+06 | 0.629907    |
| Wilmot 54-7                | 54007 |   595097 |   589813 |   530510 |   467833 |   559904 |   570516 |   515474 |   494762 |   482172 |   458576 |   550578 |   623114 |   458576 |      1.49632e+06 | 0.30647     |
| Winner 59-2                | 59002 |  2148211 |  2229405 |  2043130 |  1857427 |  2238432 |  2191943 |  2031067 |  1938573 |  1841019 |  1810454 |  2036103 |  2011261 |  1810454 |      4.44693e+06 | 0.407124    |
| Wolsey-Wessington 02-6     |  2006 |   609421 |   576246 |   574045 |   457840 |   682142 |   653728 |   538323 |   502562 |   426553 |   369547 |   567219 |   737501 |   369547 |      2.38871e+06 | 0.154706    |
| Woonsocket 55-4            | 55004 |  1220584 |  1207898 |  1136541 |  1017593 |  1179922 |  1167307 |  1093779 |  1089801 |  1056233 |  1005715 |  1153375 |  1266340 |  1005715 |      1.5376e+06  | 0.65408     |
| Yankton 63-3               | 63003 |  5143284 |  4839280 |  4492012 |  3928934 |  5796855 |  5670097 |  5224895 |  5063416 |  4710229 |  4446569 |  6128049 |  6762477 |  3928934 |      1.43304e+07 | 0.274167    |



label: Q=O/P
labeled_formulas: Q=O/P
output: {"Arithmetic-Relationship": ["Q=O/P"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_423722___xlsx_f62f6bb2a01d94268b8d390f9edda5176ca63c99.xlsx___line_773