An integer x_s (0 ≤ x_s ≤ 10^4).
An integer y_s (0 ≤ y_s ≤ 10^4).
An integer x_g (0 ≤ x_g ≤ 10^4).
An integer y_g (0 ≤ y_g ≤ 10^4).
An integer N (3 ≤ N ≤ 100).
A list of N tuples, where each tuple consists of two integers x_i and y_i (0 ≤ x_i, y_i ≤ 10^4).

### Example Input:

```
0 0
4 0
4
1 1
2 1
3 3
1 2
```

### Function Signature:
Write a function f(x_s, y_s, x_g, y_g, N, coordinates) that takes in the input.
def f(x_s: int, y_s: int, x_g: int, y_g: int, N: int, coordinates: List[Tuple[int, int]]): 
    ''' 
    x_s: an integer
    y_s: an integer
    x_g: an integer
    y_g: an integer
    N: an integer
    coordinates: a list of tuples with two integers each
    '''