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 |
|----:|----:|:-------------------------------------------------------------------------------------|-------:|------:|---------:|----:|----:|----:|---------:|---------:|
|   1 | 964 | Chief Registrar Births & Deaths -cum-Director Health Services                        |     98 |    98 |     2646 |   0 |   0 |   0 |     2646 |     2646 |
|   3 | 623 | Andhra Bank                                                                          |   3446 |     0 |   172300 |   0 |   0 |   0 |   172300 |   172300 |
|   5 | 647 | Axis Bank Ltd                                                                        |   1575 |     0 |    78750 |   0 |   0 |   0 |    78750 |    78750 |
|   6 | 630 | Bandhan Bank Ltd                                                                     |    225 |     0 |    11250 |   0 |   0 |   0 |    11250 |    11250 |
|   8 | 648 | Bank of Baroda_New_648                                                               |    281 |     0 |    14050 |   0 |   0 |   0 |    14050 |    14050 |
|   9 | 602 | Bank Of India                                                                        |    203 |   152 |     6654 |   0 |   0 |   0 |     6654 |     6654 |
|  11 | 662 | BANK OF MAHARASHTRA_NEW_662                                                          |   2302 |     0 |   115100 |   0 |   0 |   0 |   115100 |   115100 |
|  12 | 671 | Baroda Rajasthan Kshetriya Gramin Bank                                               |   1281 |     0 |    64050 |   0 |   0 |   0 |    64050 |    64050 |
|  13 | 670 | BARODA UTTAR PRADESH GRAMIN BANK                                                     |   2873 |     0 |   143650 |   0 |   0 |   0 |   143650 |   143650 |
|  15 | 657 | Canara Bank_New_657                                                                  |   1261 |     0 |    63050 |   0 |   0 |   0 |    63050 |    63050 |
|  16 | 631 | Catholic Syrian Bank                                                                 |     65 |     0 |     3250 |   0 |   0 |   0 |     3250 |     3250 |
|  17 | 650 | Central Bank of India_New_650                                                        |   9777 |     0 |   488850 |   0 |   0 |   0 |   488850 |   488850 |
|  18 | 632 | City Union Bank Limited                                                              |   1305 |     0 |    65250 |   0 |   0 |   0 |    65250 |    65250 |
|  20 | 212 | Commissioner Nagaland                                                                |    461 |     0 |    23050 |   0 |   0 |   0 |    23050 |    23050 |
|  21 | 604 | Corporation Bank                                                                     |   1038 |     0 |    51900 |   0 |   0 |   0 |    51900 |    51900 |
|  22 | 206 | CSC e-Governance Services India Limited                                              | 565138 |  2767 | 28193259 |   0 |   0 |   0 | 28193259 | 28193259 |
|  23 | 151 | D.C. KURUNG KUMEY                                                                    |    354 |     0 |    17700 |   0 |   0 |   0 |    17700 |    17700 |
|  24 | 164 | DC  Tirap District                                                                   |    528 |     0 |    26400 |   0 |   0 |   0 |    26400 |    26400 |
|  25 | 154 | DC Aalo                                                                              |    105 |     0 |     5250 |   0 |   0 |   0 |     5250 |     5250 |
|  26 | 158 | DC Dibang Valley                                                                     |      1 |     0 |       50 |   0 |   0 |   0 |       50 |       50 |
|  27 | 147 | DC East Kameng                                                                       |    260 |     0 |    13000 |   0 |   0 |   0 |    13000 |    13000 |
|  28 | 156 | DC East Siang                                                                        |    120 |     0 |     6000 |   0 |   0 |   0 |     6000 |     6000 |
|  29 | 149 | DC ITANAGAR CAPITAL COMPLEX                                                          |   1003 |     0 |    50150 |   0 |   0 |   0 |    50150 |    50150 |
|  30 | 160 | DC LOHIT                                                                             |     36 |     0 |     1800 |   0 |   0 |   0 |     1800 |     1800 |
|  31 | 165 | DC Longding                                                                          |     92 |     0 |     4600 |   0 |   0 |   0 |     4600 |     4600 |
|  32 | 159 | DC Lower Dibang                                                                      |    218 |     0 |    10900 |   0 |   0 |   0 |    10900 |    10900 |
|  33 | 150 | DC LOWER SUBANSIRI                                                                   |     13 |     0 |      650 |   0 |   0 |   0 |      650 |      650 |
|  34 | 162 | DC NAMSAI                                                                            |    256 |     0 |    12800 |   0 |   0 |   0 |    12800 |    12800 |
|  35 | 148 | DC PAPUMPARE                                                                         |   1195 |     0 |    59750 |   0 |   0 |   0 |    59750 |    59750 |
|  36 | 155 | DC Siang                                                                             |     23 |     0 |     1150 |   0 |   0 |   0 |     1150 |     1150 |
|  37 | 157 | DC Upper Siang District                                                              |     16 |     0 |      800 |   0 |   0 |   0 |      800 |      800 |
|  38 | 153 | DC Upper Subansiri                                                                   |    701 |     0 |    35050 |   0 |   0 |   0 |    35050 |    35050 |
|  39 | 146 | DC West Kameng                                                                       |    813 |     0 |    40650 |   0 |   0 |   0 |    40650 |    40650 |
|  40 | 633 | DCB Bank                                                                             |    198 |     0 |     9900 |   0 |   0 |   0 |     9900 |     9900 |
|  41 | 812 | Delhi - NE DC                                                                        |    182 |     0 |     9100 |   0 |   0 |   0 |     9100 |     9100 |
|  43 | 664 | Dena Bank_New_664                                                                    |   9155 |     2 |   457704 |   0 |   0 |   0 |   457704 |   457704 |
|  44 | 815 | Department of Information Technology Govt of Jharkhand                               |   1013 |     1 |    50627 |   0 |   0 |   0 |    50627 |    50627 |
|  45 | 842 | Department of WCD, Haryana                                                           |     17 |    17 |      459 |   0 |   0 |   0 |      459 |      459 |
|  46 | 108 | Dept of ITC Govt of Rajasthan                                                        |  87502 |    56 |  4373812 |   0 |   0 |   0 |  4373812 |  4373812 |
|  47 | 163 | DEPUTY COMMISSIONER CHANGLANG                                                        |    600 |     0 |    30000 |   0 |   0 |   0 |    30000 |    30000 |
|  48 | 152 | DEPUTY COMMISSIONER KRA DAADI                                                        |     33 |     0 |     1650 |   0 |   0 |   0 |     1650 |     1650 |
|  49 | 145 | DEPUTY COMMISSIONER TAWANG                                                           |    108 |     0 |     5400 |   0 |   0 |   0 |     5400 |     5400 |
|  50 | 161 | Deputy Commissioner, Anjaw                                                           |     55 |     0 |     2750 |   0 |   0 |   0 |     2750 |     2750 |
|  51 | 645 | Dhanlaxmi Bank                                                                       |      8 |     0 |      400 |   0 |   0 |   0 |      400 |      400 |
|  52 | 952 | Director General Health Services,Health Deptt, Haryana                               |   2662 |  2662 |    71874 |   0 |   0 |   0 |    71874 |    71874 |
|  53 | 955 | Director Health and Family Welfare, UT                                               |   1569 |  1569 |    42363 |   0 |   0 |   0 |    42363 |    42363 |
|  54 | 956 | Directorate of Health Services, A&N Islands                                          |      8 |     8 |      216 |   0 |   0 |   0 |      216 |      216 |
|  55 | 957 | Directorate of Public Health and Family Welfare, Govt of Andhra Pradesh              |    807 |   807 |    21789 |   0 |   0 |   0 |    21789 |    21789 |
|  56 | 844 | Directorate of Woman and Child Development, Government of Himachal Pradesh           |     98 |    98 |     2646 |   0 |   0 |   0 |     2646 |     2646 |
|  57 | 217 | DIT Lakshadweep                                                                      |     28 |     0 |     1400 |   0 |   0 |   0 |     1400 |     1400 |
|  58 | 167 | DY. COMMISSIONER SHAHDARA                                                            |    120 |     0 |     6000 |   0 |   0 |   0 |     6000 |     6000 |
|  60 | 841 | Education Department, Govt. of Gujarat                                               |  11897 |     0 |   594850 |   0 |   0 |   0 |   594850 |   594850 |
|  61 | 986 | Electronics & Information Technology E&IT Department Government of Chhattisgarh GoCG |  12840 |   236 |   636572 |   0 |   0 |   0 |   636572 |   636572 |
|  63 | 103 | FCS Govt of Punjab                                                                   |  22879 | 12496 |   856542 |   0 |   0 |   0 |   856542 |   856542 |
|  64 | 634 | Federal Bank                                                                         |    240 |     0 |    12000 |   0 |   0 |   0 |    12000 |    12000 |
|  65 | 218 | General Administration Department                                                    |   9790 |     0 |   489500 |   0 |   0 |   0 |   489500 |   489500 |
|  66 | 130 | Govt of Goa                                                                          |    672 |   125 |    30725 |   0 |   0 |   0 |    30725 |    30725 |
|  68 | 102 | Govt of Himachal Pradesh                                                             |   1089 |   350 |    46400 |   0 |   0 |   0 |    46400 |    46400 |
|  70 | 132 | Govt of Kerala                                                                       |  39040 |  2829 |  1886933 |   0 |   0 |   0 |  1886933 |  1886933 |
|  71 | 127 | Govt of Maharashtra                                                                  |  76381 |     0 |  3819050 |   0 |   0 |   0 |  3819050 |  3819050 |
|  72 | 111 | Govt of Sikkim - Dept of Econo                                                       |    338 |     3 |    16831 |   0 |   0 |   0 |    16831 |    16831 |
|  73 | 138 | Govt of UT of Chandigarh                                                             |    610 |     0 |    30500 |   0 |   0 |   0 |    30500 |    30500 |
|  74 | 214 | Govt. of Mizoram                                                                     |   2475 |     0 |   123750 |   0 |   0 |   0 |   123750 |   123750 |
|  75 | 635 | HDFC Bank Limited                                                                    |    684 |     0 |    34200 |   0 |   0 |   0 |    34200 |    34200 |
|  76 | 636 | ICICI Bank Limited                                                                   |    582 |     0 |    29100 |   0 |   0 |   0 |    29100 |    29100 |
|  78 | 637 | IDFC BANK LIMITED                                                                    |    298 |     0 |    14900 |   0 |   0 |   0 |    14900 |    14900 |
|  79 | 651 | Indian Bank_New_651                                                                  |   5802 |     2 |   290054 |   0 |   0 |   0 |   290054 |   290054 |
|  80 | 659 | INDIAN OVERSEAS BANK_NEW_659                                                         |   2482 |     0 |   124100 |   0 |   0 |   0 |   124100 |   124100 |
|  81 | 804 | Indiapost                                                                            |   2476 |     0 |   123800 |   0 |   0 |   0 |   123800 |   123800 |
|  82 | 638 | IndusInd Bank                                                                        |    374 |     0 |    18700 |   0 |   0 |   0 |    18700 |    18700 |
|  84 | 818 | Information Technology Electronics and Communication Department, Govt of Telangana   |   8383 |     0 |   419150 |   0 |   0 |   0 |   419150 |   419150 |
|  85 | 101 | Jammu and Kashmir Bank                                                               |   2231 |     0 |   111550 |   0 |   0 |   0 |   111550 |   111550 |
|  86 | 639 | Karnataka Bank                                                                       |     83 |     0 |     4150 |   0 |   0 |   0 |     4150 |     4150 |
|  87 | 640 | Karur Vysya Bank                                                                     |   1288 |    34 |    63618 |   0 |   0 |   0 |    63618 |    63618 |
|  88 | 628 | KotakMahindra Bank                                                                   |   3877 |     0 |   193850 |   0 |   0 |   0 |   193850 |   193850 |
|  89 | 820 | Madhya Pradesh State Electronics Development Corporation Ltd.                        |  21775 |    91 |  1086657 |   0 |   0 |   0 |  1086657 |  1086657 |
|  92 | 143 | Odisha Computer Application Center                                                   |  16519 |   597 |   812219 |   0 |   0 |   0 |   812219 |   812219 |
|  94 | 660 | Punjab & Sind Bank_New_660                                                           |     38 |     0 |     1900 |   0 |   0 |   0 |     1900 |     1900 |
|  97 | 653 | Punjab National Bank_NEW_653                                                         |  24837 |     0 |  1241850 |   0 |   0 |   0 |  1241850 |  1241850 |
|  98 | 642 | RBL Bank Limited                                                                     |    293 |     0 |    14650 |   0 |   0 |   0 |    14650 |    14650 |
|  99 | 116 | RDD Govt of Tripura                                                                  |    782 |     0 |    39100 |   0 |   0 |   0 |    39100 |    39100 |
| 100 | 169 | Rural Development Department Bihar-1                                                 |  31646 |     8 |  1582116 |   0 |   0 |   0 |  1582116 |  1582116 |
| 101 | 110 | Rural Development Dept, Govt. of Bihar                                               |   7913 |   944 |   373938 |   0 |   0 |   0 |   373938 |   373938 |
| 102 | 141 | Secretery IT,J&K                                                                     |  22154 |     0 |  1107700 |   0 |   0 |   0 |  1107700 |  1107700 |
| 103 | 219 | Social Welfare Department, Govt of Mizoram                                           |    129 |   129 |     3483 |   0 |   0 |   0 |     3483 |     3483 |
| 104 | 830 | Social Welfare Deptt.,Govt of Bihar                                                  |   2098 |  2098 |    56646 |   0 |   0 |   0 |    56646 |    56646 |
| 106 | 643 | South Indian Bank                                                                    |   1078 |     0 |    53900 |   0 |   0 |   0 |    53900 |    53900 |
| 111 | 984 | State Project Director SSA J&K                                                       |    274 |     0 |    13700 |   0 |   0 |   0 |    13700 |    13700 |
| 112 | 658 | Syndicate Bank_New_658                                                               |   9672 |     0 |   483600 |   0 |   0 |   0 |   483600 |   483600 |
| 113 | 208 | Tamil Nadu eGovernance Agency                                                        |  34327 |  4469 |  1613563 |   0 |   0 |   0 |  1613563 |  1613563 |
| 114 | 644 | Tamil Nadu Mercantile Bank                                                           |     32 |     0 |     1600 |   0 |   0 |   0 |     1600 |     1600 |
| 115 | 641 | The Nainital Bank Ltd                                                                |    565 |     0 |    28250 |   0 |   0 |   0 |    28250 |    28250 |
| 116 | 953 | U P Electronics Corporation Limited                                                  |   7882 |     5 |   393985 |   0 |   0 |   0 |   393985 |   393985 |
| 117 | 951 | U.P. Development Systems Corporation Ltd                                             |  98578 |   532 |  4916664 |   0 |   0 |   0 |  4916664 |  4916664 |
| 118 | 620 | UCO BANK                                                                             |    141 |     0 |     7050 |   0 |   0 |   0 |     7050 |     7050 |
| 120 | 656 | Union Bank Of India_New_656                                                          |   3434 |     0 |   171700 |   0 |   0 |   0 |   171700 |   171700 |
| 121 | 655 | United Bank Of India_New_655                                                         |     76 |     0 |     3800 |   0 |   0 |   0 |     3800 |     3800 |
| 122 | 126 | UT Govt. Of Dadra & Nagar Haveli                                                     |    354 |   267 |    11559 |   0 |   0 |   0 |    11559 |    11559 |
| 123 | 125 | UT Of Daman and Diu                                                                  |    377 |    91 |    16757 |   0 |   0 |   0 |    16757 |    16757 |
| 124 | 134 | UT of Puducherry                                                                     |   1281 |   845 |    44615 |   0 |   0 |   0 |    44615 |    44615 |
| 126 | 619 | Vijaya Bank                                                                          |   1900 |     0 |    95000 |   0 |   0 |   0 |    95000 |    95000 |
| 127 | 852 | WCD Govt. of MP                                                                      |   1962 |  1962 |    52974 |   0 |   0 |   0 |    52974 |    52974 |
| 128 | 856 | wcddelhi                                                                             |   7647 |  7647 |   206469 |   0 |   0 |   0 |   206469 |   206469 |
| 129 | 840 | Women & Child Development, Govt. of Gujarat                                          |  26540 | 26540 |   716580 |   0 |   0 |   0 |   716580 |   716580 |
| 130 | 846 | Women and Child Development Govt. of Jharkhand                                       |    921 |   921 |    24867 |   0 |   0 |   0 |    24867 |    24867 |
| 131 | 646 | YES Bank Limited                                                                     |   1920 |     0 |    96000 |   0 |   0 |   0 |    96000 |    96000 |



labeled_formulas: H=A*G
I=A*G
I=A*H
H=B*G
I=B*G
I=B*H
H=D*G
I=D*G
H=D*I
H=E*G
I=E*G
H=E*I
H=F*G
I=F*G
J=F+G
K=F+G
H=F*I
J=F+I
K=F+I
H=G*J
H=G*K
I=G*J
I=G*K
K=G+J
H=I*J
H=I*K
K=H+J
K=I+J
H=(A+B)*G
I=(A+B)*G
I=(A+B)*H
H=(A*D)*G
I=(A+D)*G
H=(A*D)*I
H=(A*E)*G
I=(A+E)*G
H=(A*E)*I
H=(A*F)*G
I=(A+F)*G
J=(A*G)+F
K=(A*G)+F
H=(A*F)*I
J=(A*H)+F
K=(A*H)+F
J=(A*I)+F
K=(A*I)+F
I=(A*H)+G
H=(A*G)*J
H=(A*G)*K
I=(A*G)*J
I=(A*G)*K
K=(A*G)+J
H=(A*I)*J
H=(A*I)*K
K=(A*H)+J
K=(A*I)+J
H=(B*D)*G
I=(B+D)*G
H=(B*D)*I
H=(B*E)*G
I=(B+E)*G
H=(B*E)*I
H=(B*F)*G
I=(B+F)*G
J=(B*G)+F
K=(B*G)+F
H=(B*F)*I
J=(B*H)+F
K=(B*H)+F
J=(B*I)+F
K=(B*I)+F
I=(B*H)+G
H=(B*G)*J
H=(B*G)*K
I=(B*G)*J
I=(B*G)*K
K=(B*G)+J
H=(B*I)*J
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_481146___xlsx_ae18c825d351a56cd07973f2d76ca65df4ed0afc.xlsx___line_516