user: ### Task:

Your job is to take a pair of parametric equations, passed in as strings, and convert them into a single rectangular equation by eliminating the parameter. Both parametric halves will represent linear equations of x as a function of time and y as a function of time respectively. 

The format of the final equation must be `Ax + By = C` or `Ax - By = C` where A and B must be positive and A, B, and C are integers. The final equation also needs to have the lowest possible whole coefficients. Omit coefficients equal to one.

The method is called `para_to_rect` or `EquationsManager.paraToRect` and takes in two strings in the form `x = at +(or -) b` and `y = ct +(or -) d` respectively, where `a` and `c` must be integers, and `b` and `d` must be positive integers. If `a` or `c` is omitted, the coefficient of _t_ is obviously assumed to be 1 (see final case in the example tests). There will NEVER be double signs in the equations inputted (For example: `"x = -12t + -18"` and `"y = -12t - -18"` won't show up.)

### Examples:

```python
para_to_rect("x = 12t + 18", "y = 8t + 7") => "2x - 3y = 15"
```

> __CALCULATION:__  
  x = 12t + 18  
  y = 8t + 7  
  2x = 24t + 36  
  3y = 24t + 21  
  2x - 3y = (24t + 36) - (24t + 21)  
  2x - 3y = 15  

```python
para_to_rect("x = -12t - 18", "y = 8t + 7") => "2x + 3y = -15"
```

> __CALCULATION:__  
  x = -12t - 18  
  y = 8t + 7  
  2x = -24t - 36  
  3y = 24t + 21  
  2x + 3y = (-24t - 36) + (24t + 21)  
  2x + 3y = -15  

```python
para_to_rect("x = -t + 12", "y = 12t - 1") => "12x + y = 143"
```

> __CALCULATION:__  
  x = -t + 12  
  y = 12t - 1  
  12x = -12t + 144  
  y   = 12t  - 1  
  12x + y = 143  

More examples in the sample test cases.

### Notes:

As you can see above, sometimes you'll need to add the two parametric equations after multiplying by the necessary values; sometimes you'll need to subtract them – just get rid of the _t_!

Answer: {"fn_name": "para_to_rect", "inputs": [["x = 12t + 18", "y = 8t + 7"], ["x = -12t + 18", "y = 8t + 7"], ["x = 12t + 18", "y = -8t + 7"], ["x = -12t + 18", "y = -8t + 7"], ["x = -t + 12", "y = 12t - 1"], ["x = -12t - 18", "y = 8t - 7"], ["x = -12t + 18", "y = 8t - 7"], ["x = -18t + 12", "y = 7t - 8"], ["x = 18t + 12", "y = 7t - 8"], ["x = 18t + 12", "y = 7t + 8"], ["x = 2t + 5", "y = 3t + 4"], ["x = -2t + 5", "y = 3t - 4"], ["x = 15t + 2", "y = 20t - 11"], ["x = 15t - 2", "y = -20t - 11"], ["x = 2t - 1", "y = 2t - 1"], ["x = -2t + 1", "y = 2t + 1"], ["x = 16t + 16", "y = 8t - 12"], ["x = 16t - 16", "y = -8t - 12"], ["x = -t + 12", "y = 2t - 3"], ["x = t + 12", "y = 2t - 3"], ["x = 6t - 99", "y = 10t - 79"], ["x = -139t + 119", "y = -89t + 12"], ["x = -93t + 104", "y = t - 77"], ["x = 148t + 3", "y = -11t + 63"], ["x = -t + 96", "y = 29t - 143"], ["x = -144t - 118", "y = -142t + 65"], ["x = -71t + 37", "y = -131t - 124"], ["x = -t + 109", "y = -54t - 118"], ["x = -73t - 59", "y = t + 132"], ["x = -90t - 42", "y = -37t + 149"], ["x = -69t - 7", "y = 117t - 59"], ["x = 14t - 145", "y = 3t + 19"], ["x = 84t + 84", "y = -36t - 41"], ["x = 138t - 139", "y = -47t - 134"], ["x = -113t - 116", "y = -72t - 124"], ["x = 103t - 106", "y = -81t - 24"], ["x = -14t + 124", "y = t - 44"], ["x = 144t - 119", "y = -29t + 69"], ["x = 125t - 4", "y = -t + 50"], ["x = -132t + 142", "y = 75t - 58"]], "outputs": [["2x - 3y = 15"], ["2x + 3y = 57"], ["2x + 3y = 57"], ["2x - 3y = 15"], ["12x + y = 143"], ["2x + 3y = -57"], ["2x + 3y = 15"], ["7x + 18y = -60"], ["7x - 18y = 228"], ["7x - 18y = -60"], ["3x - 2y = 7"], ["3x + 2y = 7"], ["4x - 3y = 41"], ["4x + 3y = -41"], ["x - y = 0"], ["x + y = 2"], ["x - 2y = 40"], ["x + 2y = -40"], ["2x + y = 21"], ["2x - y = 27"], ["5x - 3y = -258"], ["89x - 139y = 8923"], ["x + 93y = -7057"], ["11x + 148y = 9357"], ["29x + y = 2641"], ["71x - 72y = -13058"], ["131x - 71y = 13651"], ["54x - y = 6004"], ["x + 73y = 9577"], ["37x - 90y = -14964"], ["39x + 23y = -1630"], ["3x - 14y = -701"], ["3x + 7y = -35"], ["47x + 138y = -25025"], ["72x - 113y = 5660"], ["81x + 103y = -11058"], ["x + 14y = -492"], ["29x + 144y = 6485"], ["x + 125y = 6246"], ["25x + 44y = 998"]]}