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 |
|----:|----:|:-----------------------------------------------------------------------------------|----:|------:|------:|--------:|-------:|----:|----:|----:|----:|--------:|----:|----:|----:|----:|----:|--------:|
|   1 | 964 | Chief Registrar Births & Deaths -cum-Director Health Services                      |   0 |   646 |   646 |   17442 |  10827 |   0 |   0 |   0 |   0 |    6615 |   0 |   0 |   0 |   0 |   0 |    6615 |
|   4 | 623 | Andhra Bank                                                                        |   0 |  6623 |     0 |  331150 | 155800 |   0 |   0 |   0 |   0 |  175350 |   0 |   0 |   0 |   0 |   0 |  175350 |
|   6 | 647 | Axis Bank Ltd                                                                      |   0 |  2305 |     0 |  115250 |  53650 |   0 |   0 |   0 |   0 |   61600 |   0 |   0 |   0 |   0 |   0 |   61600 |
|   7 | 630 | Bandhan Bank Ltd                                                                   |   0 |   311 |     0 |   15550 |   6050 |   0 |   0 |   0 |   0 |    9500 |   0 |   0 |   0 |   0 |   0 |    9500 |
|   9 | 648 | Bank of Baroda_New_648                                                             |   0 |  1966 |     0 |   98300 |  56400 |   0 |   0 |   0 |   0 |   41900 |   0 |   0 |   0 |   0 |   0 |   41900 |
|  10 | 602 | Bank Of India                                                                      |   0 |  4872 |  4692 |  135684 |   2285 |   0 |   0 |   0 |   0 |  133399 |   0 |   0 |   0 |   0 |   0 |  133399 |
|  12 | 662 | BANK OF MAHARASHTRA_NEW_662                                                        |   0 |  2599 |     0 |  129950 |  42100 |   0 |   0 |   0 |   0 |   87850 |   0 |   0 |   0 |   0 |   0 |   87850 |
|  13 | 671 | Baroda Rajasthan Kshetriya Gramin Bank                                             |   0 |  2447 |     0 |  122350 |  53050 |   0 |   0 |   0 |   0 |   69300 |   0 |   0 |   0 |   0 |   0 |   69300 |
|  14 | 670 | BARODA UTTAR PRADESH GRAMIN BANK                                                   |   0 | 14340 |     0 |  717000 | 258200 |   0 |   0 |   0 |   0 |  458800 |   0 |   0 |   0 |   0 |   0 |  458800 |
|  16 | 657 | Canara Bank_New_657                                                                |   0 |  5630 |     0 |  281500 | 200700 |   0 |   0 |   0 |   0 |   80800 |   0 |   0 |   0 |   0 |   0 |   80800 |
|  17 | 631 | Catholic Syrian Bank                                                               |   0 |    94 |     0 |    4700 |   2900 |   0 |   0 |   0 |   0 |    1800 |   0 |   0 |   0 |   0 |   0 |    1800 |
|  18 | 650 | Central Bank of India_New_650                                                      |   0 | 14984 |     0 |  749200 | 223050 |   0 |   0 |   0 |   0 |  526150 |   0 |   0 |   0 |   0 |   0 |  526150 |
|  19 | 632 | City Union Bank Limited                                                            |   0 |  2634 |     1 |  131677 |      0 |   0 |   0 |   0 |   0 |  131677 |   0 |   0 |   0 |   0 |   0 |  131677 |
|  21 | 212 | Commissioner Nagaland                                                              |   0 |  2662 |     0 |  133100 |  45850 |   0 |   0 |   0 |   0 |   87250 |   0 |   0 |   0 |   0 |   0 |   87250 |
|  22 | 604 | Corporation Bank                                                                   |   0 |  4509 |     0 |  225450 | 100800 |   0 |   0 |   0 |   0 |  124650 |   0 |   0 |   0 |   0 |   0 |  124650 |
|  24 | 151 | D.C. KURUNG KUMEY                                                                  |   0 |   251 |     0 |   12550 |      0 |   0 |   0 |   0 |   0 |   12550 |   0 |   0 |   0 |   0 |   0 |   12550 |
|  25 | 164 | DC  Tirap District                                                                 |   0 |   702 |     0 |   35100 |   3900 |   0 |   0 |   0 |   0 |   31200 |   0 |   0 |   0 |   0 |   0 |   31200 |
|  26 | 154 | DC Aalo                                                                            |   0 |   294 |     0 |   14700 |   3000 |   0 |   0 |   0 |   0 |   11700 |   0 |   0 |   0 |   0 |   0 |   11700 |
|  27 | 158 | DC Dibang Valley                                                                   |   0 |    29 |     0 |    1450 |      0 |   0 |   0 |   0 |   0 |    1450 |   0 |   0 |   0 |   0 |   0 |    1450 |
|  28 | 147 | DC East Kameng                                                                     |   0 |   442 |     0 |   22100 |      0 |   0 |   0 |   0 |   0 |   22100 |   0 |   0 |   0 |   0 |   0 |   22100 |
|  29 | 156 | DC East Siang                                                                      |   0 |   316 |     0 |   15800 |      0 |   0 |   0 |   0 |   0 |   15800 |   0 |   0 |   0 |   0 |   0 |   15800 |
|  31 | 160 | DC LOHIT                                                                           |   0 |   218 |     0 |   10900 |   3300 |   0 |   0 |   0 |   0 |    7600 |   0 |   0 |   0 |   0 |   0 |    7600 |
|  32 | 165 | DC Longding                                                                        |   0 |   347 |     0 |   17350 |   1250 |   0 |   0 |   0 |   0 |   16100 |   0 |   0 |   0 |   0 |   0 |   16100 |
|  33 | 159 | DC Lower Dibang                                                                    |   0 |   236 |     0 |   11800 |      0 |   0 |   0 |   0 |   0 |   11800 |   0 |   0 |   0 |   0 |   0 |   11800 |
|  34 | 150 | DC LOWER SUBANSIRI                                                                 |   0 |    57 |     0 |    2850 |      0 |   0 |   0 |   0 |   0 |    2850 |   0 |   0 |   0 |   0 |   0 |    2850 |
|  35 | 162 | DC NAMSAI                                                                          |   0 |   521 |     0 |   26050 |  10950 |   0 |   0 |   0 |   0 |   15100 |   0 |   0 |   0 |   0 |   0 |   15100 |
|  37 | 155 | DC Siang                                                                           |   0 |   101 |     0 |    5050 |   1900 |   0 |   0 |   0 |   0 |    3150 |   0 |   0 |   0 |   0 |   0 |    3150 |
|  38 | 157 | DC Upper Siang District                                                            |   0 |   159 |     0 |    7950 |   1300 |   0 |   0 |   0 |   0 |    6650 |   0 |   0 |   0 |   0 |   0 |    6650 |
|  39 | 153 | DC Upper Subansiri                                                                 |   0 |  1267 |     0 |   63350 |  10600 |   0 |   0 |   0 |   0 |   52750 |   0 |   0 |   0 |   0 |   0 |   52750 |
|  40 | 146 | DC West Kameng                                                                     |   0 |   972 |     0 |   48600 |      0 |   0 |   0 |   0 |   0 |   48600 |   0 |   0 |   0 |   0 |   0 |   48600 |
|  41 | 633 | DCB Bank                                                                           |   0 |   833 |     0 |   41650 |  19300 |   0 |   0 |   0 |   0 |   22350 |   0 |   0 |   0 |   0 |   0 |   22350 |
|  44 | 664 | Dena Bank_New_664                                                                  |   0 | 21021 |     0 | 1051050 | 558850 |   0 |   0 |   0 |   0 |  492200 |   0 |   0 |   0 |   0 |   0 |  492200 |
|  45 | 815 | Department of Information Technology Govt of Jharkhand                             |   0 |  2749 |    14 |  137128 |      0 |   0 |   0 |   0 |   0 |  137128 |   0 |   0 |   0 |   0 |   0 |  137128 |
|  46 | 842 | Department of WCD, Haryana                                                         |   0 |   276 |   276 |    7452 |      0 |   0 |   0 |   0 |   0 |    7452 |   0 |   0 |   0 |   0 |   0 |    7452 |
|  48 | 163 | DEPUTY COMMISSIONER CHANGLANG                                                      |   0 |  1406 |     0 |   70300 |      0 |   0 |   0 |   0 |   0 |   70300 |   0 |   0 |   0 |   0 |   0 |   70300 |
|  49 | 152 | DEPUTY COMMISSIONER KRA DAADI                                                      |   0 |    46 |     0 |    2300 |    650 |   0 |   0 |   0 |   0 |    1650 |   0 |   0 |   0 |   0 |   0 |    1650 |
|  50 | 145 | DEPUTY COMMISSIONER TAWANG                                                         |   0 |    27 |     0 |    1350 |    150 |   0 |   0 |   0 |   0 |    1200 |   0 |   0 |   0 |   0 |   0 |    1200 |
|  51 | 161 | Deputy Commissioner, Anjaw                                                         |   0 |    61 |     0 |    3050 |      0 |   0 |   0 |   0 |   0 |    3050 |   0 |   0 |   0 |   0 |   0 |    3050 |
|  52 | 645 | Dhanlaxmi Bank                                                                     |   0 |     1 |     0 |      50 |      0 |   0 |   0 |   0 |   0 |      50 |   0 |   0 |   0 |   0 |   0 |      50 |
|  53 | 952 | Director General Health Services,Health Deptt, Haryana                             |   0 |  6724 |  6724 |  181548 |  48114 |   0 |   0 |   0 |   0 |  133434 |   0 |   0 |   0 |   0 |   0 |  133434 |
|  54 | 955 | Director Health and Family Welfare, UT                                             |   0 |  2178 |  2178 |   58806 |      0 |   0 |   0 |   0 |   0 |   58806 |   0 |   0 |   0 |   0 |   0 |   58806 |
|  55 | 956 | Directorate of Health Services, A&N Islands                                        |   0 |    10 |    10 |     270 |     54 |   0 |   0 |   0 |   0 |     216 |   0 |   0 |   0 |   0 |   0 |     216 |
|  56 | 957 | Directorate of Public Health and Family Welfare, Govt of Andhra Pradesh            |   0 |   699 |   699 |   18873 |   5184 |   0 |   0 |   0 |   0 |   13689 |   0 |   0 |   0 |   0 |   0 |   13689 |
|  57 | 843 | Directorate of Secondary Education, Haryana                                        |   0 |     5 |     0 |     250 |      0 |   0 |   0 |   0 |   0 |     250 |   0 |   0 |   0 |   0 |   0 |     250 |
|  58 | 844 | Directorate of Woman and Child Development, Government of Himachal Pradesh         |   0 |   274 |   274 |    7398 |   1566 |   0 |   0 |   0 |   0 |    5832 |   0 |   0 |   0 |   0 |   0 |    5832 |
|  59 | 217 | DIT Lakshadweep                                                                    |   0 |   217 |     0 |   10850 |    250 |   0 |   0 |   0 |   0 |   10600 |   0 |   0 |   0 |   0 |   0 |   10600 |
|  60 | 167 | DY. COMMISSIONER SHAHDARA                                                          |   0 |   321 |     0 |   16050 |      0 |   0 |   0 |   0 |   0 |   16050 |   0 |   0 |   0 |   0 |   0 |   16050 |
|  61 | 841 | Education Department, Govt. of Gujarat                                             |   0 | 20651 |     0 | 1032550 | 741050 |   0 |   0 |   0 |   0 |  291500 |   0 |   0 |   0 |   0 |   0 |  291500 |
|  64 | 103 | FCS Govt of Punjab                                                                 |   0 | 41033 | 13370 | 1744140 | 659686 |   0 |   0 |   0 |   0 | 1084454 |   0 |   0 |   0 |   0 |   0 | 1084454 |
|  65 | 634 | Federal Bank                                                                       |   0 |   255 |     0 |   12750 |   3550 |   0 |   0 |   0 |   0 |    9200 |   0 |   0 |   0 |   0 |   0 |    9200 |
|  66 | 218 | General Administration Department                                                  |   0 | 27443 |     0 | 1372150 | 381450 |   0 |   0 |   0 |   0 |  990700 |   0 |   0 |   0 |   0 |   0 |  990700 |
|  67 | 130 | Govt of Goa                                                                        |   0 |  3033 |  1511 |  116897 |  38707 |   0 |   0 |   0 |   0 |   78190 |   0 |   0 |   0 |   0 |   0 |   78190 |
|  69 | 102 | Govt of Himachal Pradesh                                                           |   0 |  3218 |  1839 |  118603 |  45516 |   0 |   0 |   0 |   0 |   73087 |   0 |   0 |   0 |   0 |   0 |   73087 |
|  73 | 111 | Govt of Sikkim - Dept of Econo                                                     |   0 |  1155 |   476 |   46802 |  18029 |   0 |   0 |   0 |   0 |   28773 |   0 |   0 |   0 |   0 |   0 |   28773 |
|  74 | 138 | Govt of UT of Chandigarh                                                           |   0 |  1100 |     0 |   55000 |  18270 |   0 |   0 |   0 |   0 |   36730 |   0 |   0 |   0 |   0 |   0 |   36730 |
|  75 | 214 | Govt. of Mizoram                                                                   |   0 |  7743 |     0 |  387150 |  72200 |   0 |   0 |   0 |   0 |  314950 |   0 |   0 |   0 |   0 |   0 |  314950 |
|  77 | 636 | ICICI Bank Limited                                                                 |   0 |   826 |     0 |   41300 |  14850 |   0 |   0 |   0 |   0 |   26450 |   0 |   0 |   0 |   0 |   0 |   26450 |
|  78 | 667 | IDBI Bank Ltd_New_667                                                              |   0 |  3554 |     0 |  177700 |  79470 |   0 |   0 |   0 |   0 |   98230 |   0 |   0 |   0 |   0 |   0 |   98230 |
|  79 | 637 | IDFC BANK LIMITED                                                                  |   0 |   527 |     0 |   26350 |  11800 |   0 |   0 |   0 |   0 |   14550 |   0 |   0 |   0 |   0 |   0 |   14550 |
|  80 | 651 | Indian Bank_New_651                                                                |   0 | 13741 |     2 |  687004 | 343550 |   0 |   0 |   0 |   0 |  343454 |   0 |   0 |   0 |   0 |   0 |  343454 |
|  81 | 659 | INDIAN OVERSEAS BANK_NEW_659                                                       |   0 |  4639 |     0 |  231950 |  91900 |   0 |   0 |   0 |   0 |  140050 |   0 |   0 |   0 |   0 |   0 |  140050 |
|  82 | 804 | Indiapost                                                                          |   0 |  3634 |     0 |  181700 |  71650 |   0 |   0 |   0 |   0 |  110050 |   0 |   0 |   0 |   0 |   0 |  110050 |
|  83 | 638 | IndusInd Bank                                                                      |   0 |   728 |     0 |   36400 |  20000 |   0 |   0 |   0 |   0 |   16400 |   0 |   0 |   0 |   0 |   0 |   16400 |
|  85 | 818 | Information Technology Electronics and Communication Department, Govt of Telangana |   0 | 17718 |     0 |  885900 | 483850 |   0 |   0 |   0 |   0 |  402050 |   0 |   0 |   0 |   0 |   0 |  402050 |
|  86 | 101 | Jammu and Kashmir Bank                                                             |   0 |  3708 |     0 |  185400 |  99350 |   0 |   0 |   0 |   0 |   86050 |   0 |   0 |   0 |   0 |   0 |   86050 |
|  87 | 639 | Karnataka Bank                                                                     |   0 |   167 |     0 |    8350 |   3800 |   0 |   0 |   0 |   0 |    4550 |   0 |   0 |   0 |   0 |   0 |    4550 |
|  88 | 640 | Karur Vysya Bank                                                                   |   0 |  2912 |    97 |  143369 |  62908 |   0 |   0 |   0 |   0 |   80461 |   0 |   0 |   0 |   0 |   0 |   80461 |
|  89 | 628 | KotakMahindra Bank                                                                 |   0 |  9081 |     0 |  454050 | 225550 |   0 |   0 |   0 |   0 |  228500 |   0 |   0 |   0 |   0 |   0 |  228500 |
|  90 | 629 | Lakshmi Vilas Bank                                                                 |   0 |   102 |     0 |    5100 |   3650 |   0 |   0 |   0 |   0 |    1450 |   0 |   0 |   0 |   0 |   0 |    1450 |
|  93 | 823 | National Institute of Electronics & Information Technology                         |   0 |     4 |     0 |     200 |    180 |   0 |   0 |   0 |   0 |      20 |   0 |   0 |   0 |   0 |   0 |      20 |
|  97 | 660 | Punjab & Sind Bank_New_660                                                         |   0 |    46 |     0 |    2300 |   1700 |   0 |   0 |   0 |   0 |     600 |   0 |   0 |   0 |   0 |   0 |     600 |
| 100 | 653 | Punjab National Bank_NEW_653                                                       |   0 | 47869 |    15 | 2393105 | 746931 |   0 |   0 |   0 |   0 | 1646174 |   0 |   0 |   0 |   0 |   0 | 1646174 |
| 101 | 642 | RBL Bank Limited                                                                   |   0 |   657 |     0 |   32850 |  18150 |   0 |   0 |   0 |   0 |   14700 |   0 |   0 |   0 |   0 |   0 |   14700 |
| 102 | 116 | RDD Govt of Tripura                                                                |   0 |  1759 |     1 |   87927 |  18000 |   0 |   0 |   0 |   0 |   69927 |   0 |   0 |   0 |   0 |   0 |   69927 |
| 106 | 219 | Social Welfare Department, Govt of Mizoram                                         |   0 |  1578 |  1578 |   42606 |      0 |   0 |   0 |   0 |   0 |   42606 |   0 |   0 |   0 |   0 |   0 |   42606 |
| 107 | 830 | Social Welfare Deptt.,Govt of Bihar                                                |   0 |  6375 |  6375 |  172125 |  63585 |   0 |   0 |   0 |   0 |  108540 |   0 |   0 |   0 |   0 |   0 |  108540 |
| 108 | 643 | South Indian Bank                                                                  |   0 |  2322 |     0 |  116100 |  54100 |   0 |   0 |   0 |   0 |   62000 |   0 |   0 |   0 |   0 |   0 |   62000 |



labeled_formulas: J=A*D
K=A*D
L=A*D
N=A*D
O=A*D
R=A*D
J=A*I
K=A*I
L=A*I
N=A*I
O=A*I
R=A*I
K=A*J
L=A*J
N=A*J
R=A*J
L=A*K
N=A*K
R=A*K
N=A*L
R=A*L
R=A*N
R=A*O
J=B*D
K=B*D
L=B*D
N=B*D
O=B*D
R=B*D
J=B*I
K=B*I
L=B*I
N=B*I
O=B*I
R=B*I
K=B*J
L=B*J
N=B*J
R=B*J
L=B*K
N=B*K
R=B*K
N=B*L
R=B*L
R=B*N
R=B*O
J=D*E
K=D*E
L=D*E
N=D*E
J=(A+B)*D
K=(A+B)*D
L=(A+B)*D
N=(A+B)*D
O=(A+B)*D
R=(A+B)*D
J=(A+B)*I
K=(A+B)*I
L=(A+B)*I
N=(A+B)*I
O=(A+B)*I
R=(A+B)*I
K=(A+B)*J
L=(A+B)*J
N=(A+B)*J
R=(A+B)*J
L=(A+B)*K
N=(A+B)*K
R=(A+B)*K
N=(A+B)*L
R=(A+B)*L
R=(A+B)*N
R=(A+B)*O
J=(A*D)*E
K=(A*D)*E
L=(A*D)*E
N=(A*D)*E
O=(A*D)*E
R=(A*D)*E
D=(A*F)*J
D=(A*F)*K
D=(A*F)*L
D=(A*F)*O
D=(A*F)*P
D=(A*F)*Q
D=(A*F)*R
J=(A*D)*G
K=(A*D)*G
L=(A*D)*G
N=(A*D)*G
O=(A*D)*G
R=(A*D)*G
J=(A*D)*H
K=(A*D)*H
L=(A*D)*H
D=(A*H)*O
D=(A*H)*P
D=(A*H)*Q
D=(A*H)*R
K=(A*D)*J
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_707768___xlsx_98c5d479fd872ec837302af6b6e4c437b101844d.xlsx___line_503