Canonicalized Input Description:

An integer N (1 ≤ N ≤ 10^3), representing some quantity or size.
An integer H (1 ≤ H ≤ 1000), representing some dimension.
An integer W (1 ≤ W ≤ 1000), representing some dimension.
A list of N integers Li (1 ≤ Li ≤ 100), representing sizes.
A list of N lists of tuples (pxij, pyij), where each tuple contains two integers (0 ≤ pxij < W, 0 ≤ pyij < H).

### Example Input:
```
3
10
10
2 3 4
[(0, 0), (1, 1)]
[(2, 2), (3, 3), (4, 4)]
[(5, 5), (6, 6), (7, 7), (8, 8)]
```

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