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 |   T |
|:------------|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|
| Alamosa     |   1 |   2 |   3 |   1 |   0 |   1 |   0 |   1 |   1 |   1 |   2 |   3 |   0 |   0 |   0 |   0 |   0 |   0 |   8 |
| Archuleta   |   0 |   2 |   2 |   0 |   4 |   4 |   0 |   0 |   0 |   0 |   1 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   7 |
| Baca        |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |
| Cheyenne    |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| Clear Creek |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| Conejos     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| Costilla    |   0 |   2 |   2 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   2 |
| Crowley     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   2 |   2 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   2 |
| Custer      |   0 |   0 |   0 |   0 |   1 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |
| Delta       |   0 |   3 |   3 |   0 |   2 |   2 |   0 |   2 |   2 |   1 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   8 |
| Dolores     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |
| Eagle       |   0 |   3 |   3 |   0 |   4 |   4 |   0 |   2 |   2 |   0 |   1 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |  10 |
| Elbert      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| Fremont     |   2 |   4 |   6 |   0 |   6 |   6 |   0 |   4 |   4 |   1 |   2 |   3 |   0 |   0 |   0 |   0 |   0 |   0 |  19 |
| Garfield    |   1 |   3 |   4 |   1 |   4 |   5 |   0 |   5 |   5 |   1 |   1 |   2 |   0 |   0 |   0 |   0 |   0 |   0 |  16 |
| Gilpin      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| Grand       |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| Gunnison    |   0 |   4 |   4 |   0 |   0 |   0 |   0 |   1 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   5 |
| Hinsdale    |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| Huerfano    |   0 |   3 |   3 |   0 |   0 |   0 |   0 |   1 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   4 |
| Jackson     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| Kiowa       |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| Kit Carson  |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |
| La Plata    |   1 |   6 |   7 |   0 |   3 |   3 |   0 |   4 |   4 |   0 |   5 |   5 |   0 |   0 |   0 |   0 |   0 |   0 |  19 |
| Lake        |   0 |   0 |   0 |   0 |   2 |   2 |   0 |   1 |   1 |   0 |   3 |   3 |   0 |   0 |   0 |   0 |   0 |   0 |   6 |
| Las Animas  |   1 |   4 |   5 |   1 |   1 |   2 |   0 |   0 |   0 |   0 |   3 |   3 |   0 |   0 |   0 |   0 |   0 |   0 |  10 |
| Lincoln     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| Logan       |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   1 |   1 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   2 |
| Mesa        |   1 |   9 |  10 |   1 |   7 |   8 |   1 |   4 |   5 |   1 |  11 |  12 |   0 |   0 |   0 |   0 |   0 |   0 |  35 |
| Mineral     |   0 |   0 |   0 |   0 |   1 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |
| Moffat      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |
| Morgan      |   1 |   1 |   2 |   0 |   0 |   0 |   0 |   2 |   2 |   1 |   1 |   2 |   0 |   0 |   0 |   0 |   0 |   0 |   6 |
| Ouray       |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| Park        |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| Phillips    |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| Pitkin      |   0 |   1 |   1 |   0 |   1 |   1 |   0 |   2 |   2 |   0 |   1 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   5 |
| Prowers     |   0 |   1 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |
| Rio Blanco  |   0 |   1 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   2 |
| Routt       |   0 |   0 |   0 |   0 |   6 |   6 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   6 |
| Saguache    |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |
| San Juan    |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| San Miguel  |   0 |   2 |   2 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   3 |
| Sedgwick    |   0 |   1 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |
| Teller      |   1 |   3 |   4 |   0 |   0 |   0 |   0 |   1 |   1 |   1 |   5 |   6 |   0 |   0 |   0 |   0 |   0 |   0 |  11 |
| Washington  |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| Yuma        |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |



labeled_formulas: G=(B*E)+F
N=(B-E)*H
O=(B-E)*H
P=(B-E)*H
Q=(B-E)*H
R=(B-E)*H
S=(B-E)*H
J=(B*H)+I
N=(B-K)*H
O=(B-K)*H
P=(B-K)*H
Q=(B-K)*H
R=(B-K)*H
S=(B-K)*H
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_37167___xlsx_906bf3d8f08ef4a01840f09a7c9f7dc5878ab9e4.xlsx___line_621