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 |
|----:|:------------------------------------------------------------------------------|----:|----:|:-----|-----:|----:|-----:|----:|----:|----:|----:|----:|----:|
|   1 | Ink refill for Brother, black                                                 | 560 |   3 | btl  | 1680 |   1 |  560 |   1 | 560 |   1 | 560 |   0 |   0 |
|   2 | Ink refill for Brother, cyan                                                  | 560 |   3 | btl  | 1680 |   1 |  560 |   1 | 560 |   1 | 560 |   0 |   0 |
|   3 | Ink refill for Brother, magenta                                               | 560 |   3 | btl  | 1680 |   1 |  560 |   1 | 560 |   1 | 560 |   0 |   0 |
|   4 | Ink refill for Brother, yellow                                                | 560 |   3 | btl  | 1680 |   1 |  560 |   1 | 560 |   1 | 560 |   0 |   0 |
|   5 | Ink refill, continous, black                                                  | 100 |   4 | btl  |  400 |   1 |  100 |   1 | 100 |   1 | 100 |   1 | 100 |
|   6 | Ink refill, continous, cyan                                                   | 100 |   4 | btl  |  400 |   1 |  100 |   1 | 100 |   1 | 100 |   1 | 100 |
|   7 | Ink refill, continous, magenta                                                | 100 |   4 | btl  |  400 |   1 |  100 |   1 | 100 |   1 | 100 |   1 | 100 |
|   8 | Ink refill, continous, yellow                                                 | 100 |   4 | btl  |  400 |   1 |  100 |   1 | 100 |   1 | 100 |   1 | 100 |
|   9 | Ballpen, 50's, black (Matrix OG-5)                                            | 430 |   3 | box  | 1290 |   1 |  430 |   1 | 430 |   1 | 430 |   0 |   0 |
|  10 | Ballpen, retracktable, black (Pilot)                                          | 700 |   2 | box  | 1400 |   1 |  700 |   0 |   0 |   1 | 700 |   0 |   0 |
|  11 | Binder clip, 1"                                                               |  70 |   4 | box  |  280 |   1 |   70 |   1 |  70 |   1 |  70 |   1 |  70 |
|  12 | Binder clip, 2"                                                               |  80 |   4 | box  |  320 |   1 |   80 |   1 |  80 |   1 |  80 |   1 |  80 |
|  13 | Binder clip, 3/4                                                              |  45 |   4 | box  |  180 |   1 |   45 |   1 |  45 |   1 |  45 |   1 |  45 |
|  14 | Bookpaper, sub20, 70g/m2, long                                                | 280 |   4 | ream | 1120 |   1 |  280 |   1 | 280 |   1 | 280 |   1 | 280 |
|  15 | Bookpaper, sub20, 70g/m2, short                                               | 250 |   4 | ream | 1000 |   1 |  250 |   1 | 250 |   1 | 250 |   1 | 250 |
|  16 | Certificate holder, short, blue                                               |  70 |   4 | pc   |  280 |   1 |   70 |   1 |  70 |   1 |  70 |   1 |  70 |
|  17 | Correction tape                                                               |  55 |   4 | pc   |  220 |   1 |   55 |   1 |  55 |   1 |  55 |   1 |  55 |
|  18 | Envelop, brown, long                                                          |   7 |  40 | pc   |  280 |  10 |   70 |  20 | 140 |  10 |  70 |   0 |   0 |
|  19 | Envelop, brown, short                                                         |   6 |  38 | pc   |  228 |  10 |   60 |  18 | 108 |  10 |  60 |   0 |   0 |
|  20 | Envelop, Expanding w/garter, blue, long                                       |  35 |  40 | pc   | 1400 |  10 |  350 |  20 | 700 |  10 | 350 |   0 |   0 |
|  22 | Folder, long ivory, 14 pts.                                                   |   7 |  40 | pc   |  280 |  10 |   70 |  20 | 140 |  10 |  70 |   0 |   0 |
|  23 | Folder, short ivory, 14 pts.                                                  |   6 |  40 | pc   |  240 |  10 |   60 |  20 | 120 |  10 |  60 |   0 |   0 |
|  24 | Glue, 130 g (Elmer's)                                                         |  59 |   8 | btl  |  472 |   3 |  177 |   3 | 177 |   2 | 118 |   0 |   0 |
|  25 | Laminating film, long, 250mic                                                 |  20 |  50 | pc   | 1000 |  20 |  400 |  20 | 400 |  10 | 200 |   0 |   0 |
|  28 | Pencil, No.2, (Mongol)                                                        |  80 |   4 | box  |  320 |   1 |   80 |   2 | 160 |   1 |  80 |   0 |   0 |
|  29 | Pentel pen, fine, black (Pilot)                                               |  55 |  10 | pc   |  550 |   0 |    0 |   5 | 275 |   5 | 275 |   0 |   0 |
|  30 | Pentel pen, broad, black (Pilot)                                              |  55 |  10 | pc   |  550 |   0 |    0 |   5 | 275 |   5 | 275 |   0 |   0 |
|  31 | Photo paper, matte, A4, 20's                                                  | 175 |   7 | pcks | 1225 |   2 |  350 |   3 | 525 |   2 | 350 |   0 |   0 |
|  32 | Record book, regular size, 300p                                               | 105 |   8 | pc   |  840 |   2 |  210 |   3 | 315 |   3 | 315 |   0 |   0 |
|  33 | Record book, regular size, 500p                                               | 130 |   8 | pc   | 1040 |   2 |  260 |   3 | 390 |   3 | 390 |   0 |   0 |
|  34 | Sign pen, 0.5, black (HBW My-gel)                                             | 470 |   3 | box  | 1410 |   1 |  470 |   1 | 470 |   1 | 470 |   0 |   0 |
|  35 | Sign pen, 0.5, green (HBW My-gel)                                             |  40 |   4 | pc   |  160 |   1 |   40 |   2 |  80 |   1 |  40 |   0 |   0 |
|  36 | Multipurpose Colored Paper, Blue, sub24, 80gsm, 250pcs/ream (Focus Bright)    | 200 |   2 | ream |  400 |   1 |  200 |   1 | 200 |   0 |   0 |   0 |   0 |
|  37 | Stamp pad ink                                                                 |  85 |   2 | btl  |  170 |   1 |   85 |   1 |  85 |   0 |   0 |   0 |   0 |
|  38 | Stapler with built in remover                                                 | 370 |   2 | pc   |  740 |   1 |  370 |   1 | 370 |   0 |   0 |   0 |   0 |
|  39 | Tape, Double sided, 1"                                                        |  65 |   8 | roll |  520 |   3 |  195 |   3 | 195 |   2 | 130 |   0 |   0 |
|  40 | Tape, masking, 1" (crocodile)                                                 |  48 |   8 | roll |  384 |   3 |  144 |   3 | 144 |   2 |  96 |   0 |   0 |
|  41 | Tape, scotch, 1" (Crocodile)                                                  |  35 |   8 | roll |  280 |   3 |  105 |   3 | 105 |   2 |  70 |   0 |   0 |
|  42 | Whiteboard pen, black (Pilot)                                                 |  75 |   8 | pc   |  600 |   3 |  225 |   3 | 225 |   2 | 150 |   0 |   0 |
|  43 | Air freshener, spray, 300ml, Lavander (Ambi pur)                              | 250 |   4 | btl  | 1000 |   1 |  250 |   1 | 250 |   1 | 250 |   1 | 250 |
|  45 | Battery, AA, 1.5v                                                             |  35 |   8 | pc   |  280 |   3 |  105 |   3 | 105 |   2 |  70 |   0 |   0 |
|  46 | Battery, AAA, 1.5v                                                            |  35 |   8 | pc   |  280 |   3 |  105 |   3 | 105 |   2 |  70 |   0 |   0 |
|  47 | Cotton balls, 300's                                                           | 135 |   4 | pack |  540 |   1 |  135 |   1 | 135 |   1 | 135 |   1 | 135 |
|  48 | Broom, soft                                                                   | 195 |   2 | pc   |  390 |   1 |  195 |   0 |   0 |   1 | 195 |   0 |   0 |
|  49 | Dishwashing liquid, 250ml., antibac                                           | 105 |  12 | btl  | 1260 |   4 |  420 |   4 | 420 |   4 | 420 |   0 |   0 |
|  50 | Disinfectant concentrate, 120ml,pine scent                                    | 285 |   4 | pc   | 1140 |   1 |  285 |   1 | 285 |   1 | 285 |   1 | 285 |
|  51 | Floor mop, wood handel                                                        | 260 |   2 | pc   |  520 |   1 |  260 |   0 |   0 |   1 | 260 |   0 |   0 |
|  52 | Garbage bag, biodegradable, 10's, big                                         | 125 |  20 | pack | 2500 |  10 | 1250 |   5 | 625 |   5 | 625 |   0 |   0 |
|  53 | Garbage bag, biodegradable, 10's, medium                                      | 105 |  20 | pack | 2100 |  10 | 1050 |   5 | 525 |   5 | 525 |   0 |   0 |
|  54 | Garbage bag, biodegradable, 10's, small                                       |  65 |  20 | pack | 1300 |  10 |  650 |   5 | 325 |   5 | 325 |   0 |   0 |
|  55 | mop head                                                                      | 300 |   4 | pc   | 1200 |   1 |  300 |   1 | 300 |   1 | 300 |   1 | 300 |
|  56 | Scrubbing pad w/foam                                                          |  45 |   8 | pc   |  360 |   3 |  135 |   3 | 135 |   2 |  90 |   0 |   0 |
|  57 | Soap, family size                                                             |  55 |   4 | pc   |  220 |   1 |   55 |   1 |  55 |   1 |  55 |   1 |  55 |
|  58 | Soap, powder, detergent, 800g                                                 | 205 |   4 | pack |  820 |   1 |  205 |   1 | 205 |   1 | 205 |   1 | 205 |
|  59 | Table rugs, white                                                             | 110 |   4 | kilo |  440 |   1 |  110 |   1 | 110 |   1 | 110 |   1 | 110 |
|  60 | Tissue paper, 3-ply, individually wrapped, classic blue, durable (Vinda/Novo) |  35 |  50 | roll | 1750 |  15 |  525 |  15 | 525 |  20 | 700 |   0 |   0 |
|  61 | Toilet brush                                                                  |  80 |   2 | pc   |  160 |   1 |   80 |   0 |   0 |   1 |  80 |   0 |   0 |
|  63 | Toilet duck, big                                                              | 190 |   4 | btl  |  760 |   1 |  190 |   1 | 190 |   2 | 380 |   0 |   0 |
|  64 | Zonrox bleach                                                                 | 260 |   2 | gal  |  520 |   1 |  260 |   0 |   0 |   1 | 260 |   0 |   0 |



label: F=D*C
H=G*C
J=I*C
L=K*C
N=M*C
labeled_formulas: F=D*C
H=G*C
J=I*C
L=K*C
N=M*C
N=H*M
N=J*M
N=L*M
N=(C*G)*M
N=(C*I)*M
N=(C*K)*M
N=(I*J)*M
output: {"Arithmetic-Relationship": ["F=D*C", "H=G*C", "J=I*C", "L=K*C", "N=M*C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_748907___xlsx_219d3299044d1fd9f61cd38a3be7b2b3bfbdc03f.xlsx___line_211