Canonicalized Input Description:

An integer N (2 ≤ N ≤ 100), representing some quantity or size.
An integer M (2 ≤ M ≤ 100), representing some other quantity or size.
An integer A (0 ≤ A ≤ 10), representing a specific count.
A grid of size N by M, where each cell contains one of the following characters: '#', '.', 'S', 'G'.

### Example Input:

```
3 3 2
S#.
...
.#G
```

### Function Signature:
Write a function f(N, M, A, grid) that takes in the input. 
def f(N: int, M: int, A: int, grid: List[str]): 
    ''' 
    N: an integer 
    M: an integer
    A: an integer
    grid: a list of strings
    '''