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 |
|:---------------------------------|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|--------:|
| Alabama, Middle District         |   0 |   0 |   0 |   0 |   1 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |  66 |  68 |   2 |   2 |  70 | 1151840 |
| Alabama, Northern District       |   0 |   0 |   0 |   7 |   2 |   0 |   7 |   0 |   0 |   0 |   1 |   0 |   3 | 119 | 139 |   0 |   0 | 139 | 2878062 |
| Alabama, Southern District       |   0 |   0 |   0 |   2 |   2 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |  31 |  36 |   0 |   0 |  36 |  844845 |
| Alaska                           |   0 |   0 |   0 |   2 |   1 |   0 |   5 |   0 |   0 |   0 |   0 |   0 |   0 |  38 |  46 |   2 |   2 |  48 |  739795 |
| Arkansas, Eastern District       |   0 |   0 |   0 |   0 |   0 |   0 |  29 |   0 |   0 |   0 |   0 |   0 |   0 |  54 |  83 |   0 |   0 |  83 | 1641446 |
| Arkansas, Western District       |   0 |   0 |   0 |   1 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   8 |  10 |   0 |   0 |  10 | 1362833 |
| California, Eastern District     |   0 |   0 |   0 |   6 |   0 |   0 |  14 |   0 |   0 |   0 |   0 |   0 |   0 |  57 |  77 |   2 |   2 |  79 | 8094481 |
| California, Northern District    |   0 |   0 |   0 |   3 |   0 |   0 |  47 |   0 |   0 |   1 |   0 |   0 |   0 |  61 | 112 |  19 |  19 | 131 | 8401302 |
| California, Southern District    |   0 |   0 |   0 |   0 |   1 |   0 |  19 |   0 |   0 |   0 |   5 |   0 |   0 |  55 |  80 |   9 |   9 |  89 | 3520515 |
| District of Columbia             |   0 |   0 |   0 |   0 |   2 |   0 |   5 |   0 |   0 |   0 |   3 |   0 |   0 |  24 |  34 |   2 |   2 |  36 |  693972 |
| Florida, Northern District       |   0 |   0 |   0 |   1 |   1 |   0 |  28 |   0 |   0 |   0 |   1 |   0 |   0 |  72 | 103 |   0 |   0 | 103 | 1858835 |
| Florida, Southern District       |   0 |   0 |   0 |   5 |   1 |   0 |  28 |   0 |   0 |   8 |   3 |   0 |   0 | 188 | 233 |  35 |  35 | 268 | 7008137 |
| Georgia, Middle District         |   0 |   0 |   0 |   2 |   0 |   0 |   3 |   0 |   0 |   0 |   0 |   0 |   0 |  17 |  22 |   0 |   0 |  22 | 2011173 |
| Georgia, Northern District       |   0 |   0 |   0 |   6 |   4 |   0 |   8 |   0 |   0 |   0 |   1 |   0 |   0 |  57 |  76 |   2 |   2 |  78 | 6831493 |
| Guam 1                           |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   5 |   5 |   0 |   0 |   5 |  159358 |
| Hawaii                           |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   2 |   0 |   0 |   0 |  16 |  19 |   0 |   0 |  19 | 1427538 |
| Idaho                            |   0 |   0 |   0 |   1 |   0 |   0 |   8 |   0 |   0 |   0 |   0 |   0 |   1 |  66 |  76 |   2 |   2 |  78 | 1716943 |
| Indiana, Northern District       |   0 |   0 |   0 |   6 |   6 |   0 |  11 |   0 |   0 |   0 |   0 |   0 |   2 | 124 | 149 |   5 |   5 | 154 | 2595142 |
| Iowa, Northern District          |   0 |   0 |   0 |   2 |   1 |   0 |   2 |   0 |   0 |   0 |   0 |   0 |   0 |  43 |  48 |   0 |   0 |  48 | 1325687 |
| Kentucky, Eastern District       |   0 |   0 |   0 |   3 |   1 |   0 |   8 |   0 |   0 |   0 |   2 |   0 |   1 |  62 |  77 |  17 |  17 |  94 | 2211234 |
| Kentucky, Western District       |   0 |   0 |   0 |   1 |   0 |   0 |  20 |   0 |   0 |   0 |   0 |   0 |   1 |  76 |  98 |   4 |   4 | 102 | 2242955 |
| Louisiana, Eastern District      |   0 |   0 |   0 |   2 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |  26 |  29 |   0 |   0 |  29 | 1687314 |
| Louisiana, Middle District       |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |  51 |  52 |   0 |   0 |  52 |  836722 |
| Louisiana, Western District      |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |  44 |  45 |   0 |   0 |  45 | 2160297 |
| Maine                            |   0 |   0 |   0 |   0 |   3 |   0 |   1 |   0 |   0 |   1 |   1 |   0 |   0 |  19 |  25 |   1 |   1 |  26 | 1335907 |
| Michigan, Western District       |   0 |   0 |   0 |   9 |   2 |   0 |  17 |   0 |   0 |   1 |   0 |   0 |   4 |  89 | 122 |   9 |   9 | 131 | 3511335 |
| Minnesota                        |   0 |   0 |   0 |   1 |   3 |   0 |   4 |   0 |   0 |   1 |   0 |   0 |   1 |  55 |  65 |   3 |   3 |  68 | 5576606 |
| Mississippi, Southern District   |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |  43 |  44 |   4 |   4 |  48 | 1870845 |
| Missouri, Eastern District       |   0 |   0 |   0 |   1 |   5 |   0 |  25 |   0 |   0 |   0 |   0 |   0 |   1 | 192 | 224 |   7 |   7 | 231 | 2936329 |
| Missouri, Western District       |   0 |   0 |   0 |   0 |   1 |   0 |  17 |   0 |   0 |   1 |   2 |   0 |   0 | 157 | 178 |   8 |   8 | 186 | 3177203 |
| Montana                          |   0 |   0 |   0 |   0 |   0 |   0 |   2 |   0 |   0 |   0 |   1 |   0 |   0 |  82 |  85 |   0 |   0 |  85 | 1050493 |
| Nevada                           |   0 |   0 |   0 |   0 |   0 |   0 |   3 |   0 |   0 |   2 |   2 |   0 |   0 |  79 |  86 |   2 |   2 |  88 | 2998039 |
| New Hampshire                    |   0 |   0 |   0 |   0 |   4 |   0 |   1 |   0 |   0 |   0 |   1 |   0 |   0 |  10 |  16 |   0 |   0 |  16 | 1342795 |
| New Jersey                       |   0 |   0 |   0 |   0 |   3 |   0 |   7 |   0 |   0 |   4 |   1 |   0 |   0 |  62 |  77 |  12 |  12 |  89 | 9005644 |
| New Mexico                       |   0 |   0 |   0 |   0 |   0 |   0 |  17 |   0 |   0 |   1 |   0 |   0 |   0 |  47 |  65 |   1 |   1 |  66 | 2088070 |
| North Carolina, Middle District  |   0 |   0 |   0 |   5 |   0 |   0 |   5 |   0 |   0 |   9 |   0 |   0 |   0 | 118 | 137 |   0 |   0 | 137 | 2982908 |
| North Carolina, Western District |   0 |   0 |   0 |   4 |   0 |   0 |  18 |   0 |   0 |   5 |   0 |   0 |   0 |  86 | 113 |   3 |   3 | 116 | 3250165 |
| North Dakota                     |   0 |   0 |   0 |   0 |   1 |   0 |   3 |   0 |   0 |   0 |   3 |   0 |   0 |  40 |  47 |   0 |   0 |  47 |  755393 |
| Northern Mariana Islands 1       |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   53883 |
| Oklahoma, Eastern District       |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |  10 |  10 |   0 |   0 |  10 |  744540 |
| Oklahoma, Western District       |   0 |   0 |   0 |   0 |   0 |   0 |   3 |   0 |   0 |   0 |   0 |   0 |   0 |  15 |  18 |   0 |   0 |  18 | 2122944 |
| Pennsylvania, Western District   |   0 |   0 |   0 |   1 |   9 |   0 |   7 |   0 |   0 |   0 |   1 |   0 |   1 |  55 |  74 |   3 |   3 |  77 | 3739642 |
| Puerto Rico                      |   0 |   0 |   0 |   0 |   0 |   0 |   9 |   0 |   0 |   3 |   1 |   0 |   0 | 178 | 191 |   4 |   4 | 195 | 3337177 |
| Rhode Island                     |   0 |   0 |   0 |   0 |   0 |   0 |   2 |   0 |   0 |   0 |   1 |   0 |   0 |  17 |  20 |   0 |   0 |  20 | 1059639 |
| South Carolina                   |   0 |   0 |   0 |   1 |   2 |   0 |  34 |   0 |   0 |   1 |   0 |   0 |   1 | 290 | 329 |   2 |   2 | 331 | 5024369 |
| South Dakota                     |   0 |   0 |   0 |   1 |   0 |   0 |   7 |   0 |   0 |   1 |   0 |   0 |   0 |  48 |  57 |   3 |   3 |  60 |  869666 |
| Tennessee, Eastern District      |   0 |   0 |   0 |   2 |   1 |   0 |  22 |   0 |   0 |   0 |   0 |   0 |   1 | 102 | 128 |  15 |  15 | 143 | 2621077 |
| Tennessee, Middle District       |   0 |   0 |   0 |   0 |   1 |   0 |   7 |   0 |   0 |   1 |   0 |   0 |   0 |  65 |  74 |   6 |   6 |  80 | 2522866 |
| U.S. Virgin Islands              |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   2 |   2 |   0 |   0 |   2 |  106405 |
| Utah                             |   0 |   0 |   0 |   0 |   0 |   0 |   5 |   0 |   0 |   0 |   1 |   0 |   0 |  36 |  42 |   1 |   1 |  43 | 3101833 |
| Washington, Eastern District     |   0 |   0 |   0 |   0 |   0 |   0 |   8 |   0 |   0 |   0 |   1 |   0 |   0 |  37 |  46 |   1 |   1 |  47 | 1603175 |
| Washington, Western District     |   0 |   0 |   0 |   1 |   2 |   0 |   3 |   0 |   0 |   0 |   2 |   0 |   0 |  51 |  59 |   3 |   3 |  62 | 5802568 |
| West Virginia, Southern District |   0 |   0 |   0 |   4 |   0 |   0 |   5 |   0 |   0 |   0 |   0 |   0 |   0 |  49 |  58 |   0 |   0 |  58 |  950524 |
| Wisconsin, Western District      |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |  13 |  14 |   0 |   0 |  14 | 2386862 |
| Wyoming                          |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |  62 |  63 |   1 |   1 |  64 |  579315 |



labeled_formulas: D=B*C
G=B*C
C=B*I
J=B*C
C=B*K
M=B*C
C=B*N
D=B*E
D=B*F
D=B*G
D=B*I
D=B*K
D=B*L
D=B*N
G=B*E
J=B*E
M=B*E
J=B*F
M=B*F
G=B*I
G=B*K
G=B*N
J=B*I
M=B*I
I=B*N
J=B*K
J=B*L
J=B*N
M=B*K
M=B*L
M=B*N
D=C*E
D=C*F
D=C*G
D=C*H
D=C*I
D=C*K
D=C*L
D=C*N
D=C*O
D=C*P
D=C*Q
D=C*R
D=C*S
D=C*T
G=C*E
J=C*E
M=C*E
G=C*F
C=F*I
D=(B*C)*E
D=(B*C)*F
D=(B*C)*H
D=(B*C)*I
D=(B*C)*K
D=(B*C)*L
D=(B*C)*N
D=(B*C)*O
D=(B*C)*P
D=(B*C)*Q
D=(B*C)*R
D=(B*C)*S
D=(B*C)*T
C=(B*E)*F
G=(B*C)*E
I=(B*C)*E
J=(B*C)*E
C=(B*E)*K
M=(B*C)*E
C=(B*E)*N
G=(B*C)*F
C=(B*F)*I
J=(B*C)*F
C=(B*F)*K
C=(B*F)*L
M=(B*C)*F
C=(B*F)*N
G=(B*C)*H
G=(B-C)*I
G=(B*C)*K
G=(B*C)*L
G=(B*C)*N
G=(B*C)*O
G=(B*C)*P
G=(B*C)*Q
G=(B*C)*R
G=(B*C)*S
G=(B*C)*T
I=(B*C)*H
J=(B*C)*H
M=(B*C)*H
C=(B*H)*N
C=(B*I)*K
C=(B*I)*L
C=(B*I)*N
C=(B*I)*O
C=(B*I)*P
C=(B*I)*Q
C=(B*I)*R
C=(B*I)*S
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_68893___xlsx_a84ad9a216bc9c0a583c4019fdb4570a3a4350b8.xlsx___line_638