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 |
|:----|:---------------|----------:|----------:|---------:|--------:|-----------:|----:|----:|----:|----:|----------:|----------:|-----------:|-----------:|
| 1   | Adair          |  16020835 |         0 |  1277734 |   96019 |    8833212 |   0 |   0 |   0 |   0 |  15397025 |  11886668 |   53511493 |   53511493 |
| 3   | Allamakee      |  17508380 |    216000 |  3287500 |   77600 |    7475100 |   0 |   0 |   0 |   0 |  39878700 |   5007700 |   73450980 |   73450980 |
| 5   | Audubon        |   4627000 |    140190 |   916400 |   64760 |    9239980 |   0 |   0 |   0 |   0 |         0 |         0 |   14988330 |   14988330 |
| 8   | Boone          |   3394039 |    313093 |  1711483 |   95800 |   15583153 |   0 |   0 |   0 |   0 |  11981642 |   2808035 |   35887245 |   35887245 |
| 9   | Bremer         |  39772280 |  98472290 |  5539600 | 2822970 |   37794330 |   0 |   0 |   0 |   0 |  80732160 |  81812660 |  346946290 |  346946290 |
| 11  | Buena Vista    |  23903770 |  16898540 |  1476470 |  250420 |    8244970 |   0 |   0 |   0 |   0 |  25411627 |  22337160 |   98522957 |   98522957 |
| 12  | Butler         |  24478340 |  45264530 |  3026380 |  336190 |    1445820 |   0 |   0 |   0 |   0 |  25380605 |         0 |   99931865 |   99931865 |
| 13  | Calhoun        |  21312279 |    281320 |  4539360 |   97100 |    3524430 |   0 |   0 |   0 |   0 |  40622416 |  19142670 |   89519575 |   89519575 |
| 14  | Carroll        |  22572450 |         0 |  1154900 | 1263300 |   36005230 |   0 |   0 |   0 |   0 |         0 |         0 |   60995880 |   60995880 |
| 15  | Cass           |  15260850 |   1778960 |   410520 |   98170 |   12416970 |   0 |   0 |   0 |   0 |  22794309 |   2393750 |   55153529 |   55153529 |
| 16  | Cedar          |  12284640 |   1578930 |   380000 |       0 |    9615458 |   0 |   0 |   0 |   0 |  27947742 |  28125050 |   79931820 |   79931820 |
| 17a | Mason City     |  49520240 |    453730 |  1072990 |  239400 |  187938388 |   0 |   0 |   0 |   0 |  37617770 |  34115512 |  310958030 |  310958030 |
| 18  | Cherokee       |  20501426 |    348163 |   975300 |   62446 |   17901386 |   0 |   0 |   0 |   0 |   6735511 |   3976067 |   50500299 |   50500299 |
| 19  | Chickasaw      |   8860500 |         0 |   564500 |   68400 |    6033900 |   0 |   0 |   0 |   0 |         0 |         0 |   15527300 |   15527300 |
| 20  | Clarke         |   4657730 |         0 |  4687250 |   51440 |    3806365 |   0 |   0 |   0 |   0 |   8278070 |   4387900 |   25868755 |   25868755 |
| 21  | Clay           |  46311840 |    909690 |  1783810 |  324220 |   14493610 |   0 |   0 |   0 |   0 | 206039430 |  61093750 |  330956350 |  330956350 |
| 22  | Clayton        |  11305957 |    686980 |        0 |  122255 |   23770094 |   0 |   0 |   0 |   0 |  30375000 |   5250000 |   71510286 |   71510286 |
| 23  | Clinton County |  15332905 |   1752175 |  2760719 |  144525 |    3795898 |   0 |   0 |   0 |   0 |  12988781 |  22989157 |   59764160 |   59764160 |
| 25  | Dallas         | 153437780 |   3552360 |  8277290 | 1852470 |  164004110 |   0 |   0 |   0 |   0 |  92422650 | 161819930 |  585366590 |  585366590 |
| 26  | Davis          |   8154880 |         0 |  2358500 |   34430 |    1540230 |   0 |   0 |   0 |   0 |  25637760 |  20252040 |   57977840 |   57977840 |
| 27  | Decatur        |   3603772 |         0 |  2263433 |       0 |     330964 |   0 |   0 |   0 |   0 |   6180264 |  12567201 |   24945634 |   24945634 |
| 28  | Delaware       |  13446890 |    598180 |  2117730 |   97680 |   47919670 |   0 |   0 |   0 |   0 |  17806130 |  29155420 |  111141700 |  111141700 |
| 31  | Dubuque County |  43213424 |   3812020 |  3383070 |  494390 |   26689627 |   0 |   0 |   0 |   0 |  76738160 |  28157610 |  182488301 |  182488301 |
| 32  | Emmet          |  15329900 |    417100 |  1640600 |  234700 |   22283000 |   0 |   0 |   0 |   0 |  21857300 |  43579250 |  105341850 |  105341850 |
| 34  | Floyd          |  25444430 |   1151090 |   450000 |   74340 |    7631770 |   0 |   0 |   0 |   0 |   2732560 |    427660 |   37911850 |   37911850 |
| 35  | Franklin       |  13736700 |    259100 |  2872300 |   81900 |   25555300 |   0 |   0 |   0 |   0 |  19697800 |  22823500 |   85026600 |   85026600 |
| 37  | Greene         |   6284000 |    267000 |  1874400 |   53600 |     213900 |   0 |   0 |   0 |   0 |  40882200 |  14937200 |   64512300 |   64512300 |
| 38  | Grundy         |  18792347 |         0 |  1622898 |    2558 |    4477090 |   0 |   0 |   0 |   0 |         0 |         0 |   24894893 |   24894893 |
| 40  | Hamilton       |  26687090 |   1900250 |  1132870 |   49280 |    3248940 |   0 |   0 |   0 |   0 |  69976040 |  38777900 |  141772370 |  141772370 |
| 41  | Hancock        |  17522120 |   1270900 |   185370 |  172974 |    3926060 |   0 |   0 |   0 |   0 |  28334060 |  11486270 |   62897754 |   62897754 |
| 42  | Hardin         |  29029180 |    514000 |  4057910 |  679680 |   10377800 |   0 |   0 |   0 |   0 |  26946650 |  39228040 |  110833260 |  110833260 |
| 43  | Harrison       |  10455572 |         0 |  3488041 |   92784 |    5929949 |   0 |   0 |   0 |   0 |  18729741 |  10978293 |   49674380 |   49674380 |
| 44  | Henry          |   7133329 |  10284777 |  1204520 |   91294 |    2082199 |   0 |   0 |   0 |   0 |         0 |         0 |   20796119 |   20796119 |
| 46  | Humboldt       |   1772885 |    372860 |  2290742 |   26610 |    7148254 |   0 |   0 |   0 |   0 |   5383911 |     14044 |   17009306 |   17009306 |
| 48  | Iowa           |  15007240 |    650290 |  2306450 |  404980 |   29300980 |   0 |   0 |   0 |   0 |  18681803 |  23659830 |   90011573 |   90011573 |
| 49  | Jackson        |  10087200 |    253200 |  1245500 |  173900 |    6176900 |   0 |   0 |   0 |   0 |  12834200 |     70100 |   30841000 |   30841000 |
| 51  | Jefferson      |  29468300 |     49100 |  2865400 |  281300 |   40061800 |   0 |   0 |   0 |   0 |  43222000 | 165762700 |  281710600 |  281710600 |
| 52  | Johnson        |  19384798 |   5156005 |   169490 | 1068520 |    3100532 |   0 |   0 |   0 |   0 |  22120273 |   8477268 |   59476886 |   59476886 |
| 52a | Iowa City      | 103411330 |   6490960 |  5857540 |  586060 |  162640845 |   0 |   0 |   0 |   0 |         0 |         0 |  278986735 |  278986735 |
| 53  | Jones          |  36079180 |   1862860 |  7156570 |  243950 |   13803445 |   0 |   0 |   0 |   0 |         0 |   6266950 |   65412955 |   65412955 |
| 54  | Keokuk         |   8421859 |    169210 |   743150 |  114390 |    4228205 |   0 |   0 |   0 |   0 |  19761236 |  14557720 |   47995770 |   47995770 |
| 55  | Kossuth        |  28085303 |    217789 |  2148714 |  271613 |   16941700 |   0 |   0 |   0 |   0 |  14833545 |  17585597 |   80084261 |   80084261 |
| 56  | Lee            |  30612550 |    770770 |  9880980 |  334310 |   16093870 |   0 |   0 |   0 |   0 |  42572490 |   1821530 |  102086500 |  102086500 |
| 57  | Linn           | 112150800 |   7666700 |  4951700 | 2048700 |   39686600 |   0 |   0 |   0 |   0 | 185109100 | 265960600 |  617574200 |  617574200 |
| 60  | Lyon           |  42558886 |    245970 |  2787320 |   42951 |    9655850 |   0 |   0 |   0 |   0 |  29359677 |  39934932 |  124585586 |  124585586 |
| 61  | Madison        |  19518000 |   1917300 |  2772300 |   96600 |    1161900 |   0 |   0 |   0 |   0 |  10360200 |    804900 |   36631200 |   36631200 |
| 62  | Mahaska        |  38040900 |  15946440 |  2951950 |  155180 |    3735920 |   0 |   0 |   0 |   0 |  20555726 |   1187110 |   82573226 |   82573226 |
| 63  | Marion         | 106231290 |  70034080 |  3695590 |  388080 |   87891910 |   0 |   0 |   0 |   0 |  60272392 |  77294560 |  405807902 |  405807902 |
| 64  | Marshall       |  22981037 |    433116 |  2111846 |  204416 |   34762949 |   0 |   0 |   0 |   0 |  59632723 |  74528658 |  194654745 |  194654745 |
| 65  | Mills          |   9630008 |    605431 |  2108592 |  237221 |    2955550 |   0 |   0 |   0 |   0 |  28561171 |    581829 |   44679802 |   44679802 |
| 67  | Monona         |  11265434 |    314486 |  1609666 |  111352 |   16731896 |   0 |   0 |   0 |   0 |  20996761 |  14447965 |   65477560 |   65477560 |
| 68  | Monroe         |   7466955 |    166311 |  1942583 |  223616 |    3027051 |   0 |   0 |   0 |   0 |  21050741 |   7053769 |   40931026 |   40931026 |
| 69  | Montgomery     |   6745880 |   1412560 |  4211770 |   69110 |   33732010 |   0 |   0 |   0 |   0 |  12622430 |    796610 |   59590370 |   59590370 |
| 70  | Muscatine      |  66186460 |         0 |  9952100 |  685510 |   57878104 |   0 |   0 |   0 |   0 |  84401840 |  44525300 |  263629314 |  263629314 |
| 71  | O'Brien        |  28865480 |         0 |   616260 |  473750 |   24257160 |   0 |   0 |   0 |   0 |  33626960 |  34794530 |  122634140 |  122634140 |
| 73  | Page           |  16659724 |    806320 |  4356950 |  654190 |   30905962 |   0 |   0 |   0 |   0 |   2797010 |     14800 |   56194956 |   56194956 |
| 75  | Plymouth       |  19858420 |    415120 |  2929870 |   68500 |    7144110 |   0 |   0 |   0 |   0 |  14511282 |   2240920 |   47168222 |   47168222 |
| 76  | Pocahontas     |   7808530 |         0 |   427976 |  159669 |    1946783 |   0 |   0 |   0 |   0 |  18518986 |   6311054 |   35172998 |   35172998 |
| 77  | Polk           | 871184020 | 457265870 | 49812580 | 2392700 | 1129057060 |   0 |   0 |   0 |   0 |         0 |         0 | 2509712230 | 2509712230 |
| 79  | Poweshiek      |  14067610 | 229173400 |        0 |   75790 |   32419620 |   0 |   0 |   0 |   0 |  34001780 |  36745840 |  346484040 |  346484040 |
| 81  | Sac            |  14984210 |    168620 |   610020 |  111790 |    3666220 |   0 |   0 |   0 |   0 |  30259920 |  11344610 |   61145390 |   61145390 |
| 82a | Davenport      | 256316070 |  82696730 | 16098880 |  820820 |  421188923 |   0 |   0 |   0 |   0 | 321990940 | 175795130 | 1274907493 | 1274907493 |
| 84  | Sioux County   | 208534580 | 185635730 |  6276950 |  186000 |  102267800 |   0 |   0 |   0 |   0 | 175596000 |  94603190 |  773100250 |  773100250 |
| 85  | Story          |  30270700 |    204400 |  1113900 |  536200 |   35291600 |   0 |   0 |   0 |   0 | 190102000 | 100344300 |  357863100 |  357863100 |
| 85a | Ames           |  75360100 |    915100 |  5523700 |  321900 |   50270300 |   0 |   0 |   0 |   0 |         0 |         0 |  132391100 |  132391100 |
| 86  | Tama           |  11375740 |         0 |  1364170 |  428050 |    4119900 |   0 |   0 |   0 |   0 |  23148452 |   1610500 |   42046812 |   42046812 |
| 90  | Wapello        |  24973289 |    584080 |  2763230 |  286560 |   18195488 |   0 |   0 |   0 |   0 | 117095664 |  87063630 |  250961941 |  250961941 |
| 92  | Washington     |  22863200 |    167900 |  1965900 |  165900 |   40067986 |   0 |   0 |   0 |   0 |  32181300 |  38226400 |  135638586 |  135638586 |
| 93  | Wayne          |   6061770 |   1283050 |  1728320 |   87320 |   11686284 |   0 |   0 |   0 |   0 |   6267643 |   8841480 |   35955867 |   35955867 |
| 95  | Winnebago      |   7854895 |         0 |  1087300 |   41420 |    1028565 |   0 |   0 |   0 |   0 |         0 |         0 |   10012180 |   10012180 |
| 96  | Winneshiek     |   8047370 |  69225550 |  5060320 |  102960 |    9489950 |   0 |   0 |   0 |   0 |  59132700 |         0 |  151058850 |  151058850 |
| 97a | Sioux City     | 166624900 | 115675300 |        0 |   24500 |  306470000 |   0 |   0 |   0 |   0 | 179119500 |  66018200 |  833932400 |  833932400 |
| 98  | Worth          |   7980099 |         0 |  2040519 |   78318 |    3975183 |   0 |   0 |   0 |   0 |         0 |         0 |   14074119 |   14074119 |
| 99  | Wright         |  21279800 |    739200 |  3649800 |  227200 |    6678900 |   0 |   0 |   0 |   0 |  30540800 |  32481800 |   95597500 |   95597500 |



labeled_formulas: I=C*H
J=C*H
K=C*H
I=D*H
J=D*H
K=D*H
I=E*H
J=E*H
K=E*H
I=F*H
J=F*H
K=F*H
I=G*H
J=G*H
K=G*H
I=H*L
I=H*M
I=H*N
I=H*O
J=H*L
J=H*M
J=H*N
J=H*O
K=H*L
K=H*M
K=H*N
K=H*O
O=H+N
I=(C*D)*H
J=(C*D)*H
K=(C*D)*H
I=(C*E)*H
J=(C*E)*H
K=(C*E)*H
I=(C*F)*H
J=(C*F)*H
K=(C*F)*H
O=(F/C)+N
I=(C+G)*H
J=(C+G)*H
K=(C+G)*H
I=(C*H)*L
I=(C*H)*M
I=(C*H)*N
I=(C*H)*O
J=(C*H)*L
J=(C*H)*M
J=(C*H)*N
J=(C*H)*O
K=(C*H)*L
K=(C*H)*M
K=(C*H)*N
K=(C*H)*O
O=(H/C)+N
I=(D*E)*H
J=(D*E)*H
K=(D*E)*H
I=(D*F)*H
J=(D*F)*H
K=(D*F)*H
I=(D*G)*H
J=(D*G)*H
K=(D*G)*H
I=(D*H)*L
I=(D*H)*M
I=(D*H)*N
I=(D*H)*O
J=(D*H)*L
J=(D*H)*M
J=(D*H)*N
J=(D*H)*O
K=(D*H)*L
K=(D*H)*M
K=(D*H)*N
K=(D*H)*O
O=(D*H)+N
I=(E*F)*H
J=(E*F)*H
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_521712___xlsx_fe4a9e9ec6c7d904e6fb34227388286f801b9cd9.xlsx___line_941