Canonicalized Input Description:

An integer N (1 ≤ N ≤ 10^3), representing some quantity or size.
An integer H (1 ≤ H ≤ 10^3), representing some dimension or height.
An integer W (1 ≤ W ≤ 10^3), representing some dimension or width.
A list of N integers L, where each integer represents a size (1 ≤ L[i] ≤ 10^3).
A list of N lists of tuples of integers (pxij, pyij), where each tuple represents coordinates (0 ≤ pxij < W, 0 ≤ pyij < H).

### Example Input:

```
2
5
5
3 4
[(0, 1), (1, 2), (2, 3)]
[(1, 1), (2, 2), (3, 3), (4, 4)]
```

### Function Signature:
Write a function f(N, H, W, L, paths) that takes in the input.
```python
def f(N: int, H: int, W: int, L: List[int], paths: List[List[Tuple[int, int]]]): 
    ''' 
    N: an integer
    H: an integer
    W: an integer
    L: a list of integers
    paths: a list of lists of tuples of integers
    '''
```