An integer x_s (0 ≤ x_s ≤ 10^4) representing a coordinate.
An integer y_s (0 ≤ y_s ≤ 10^4) representing a coordinate.
An integer x_g (0 ≤ x_g ≤ 10^4) representing a coordinate.
An integer y_g (0 ≤ y_g ≤ 10^4) representing a coordinate.
An integer N (3 ≤ N ≤ 100) representing some quantity or size.
A list of N tuples, where each tuple contains two integers (x_i, y_i) (0 ≤ x_i, y_i ≤ 10^4) representing coordinates.

### 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. 

```python
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, where each tuple contains two integers
    '''
```