Canonicalized Input Description:

An integer \(N\) (3 ≤ \(N\) ≤ 500), representing some quantity or size.
An integer \(M\) (max(3, \(N\) - 1) ≤ \(M\) ≤ 30000), representing some quantity or size.
A list of \(M\) tuples \((a_i, b_i)\), where each tuple contains two integers and \(1 ≤ a_i, b_i ≤ N\).

### Example Input:

```
3 3
1 2
2 3
3 1
```

### Function Signature:
Write a function f(N, M, edges) that takes in the input.
```python
def f(N: int, M: int, edges: List[Tuple[int, int]]):
    '''
    N: an integer
    M: an integer
    edges: a list of tuples with two integers each
    '''