Please solve the programming task below using a self-contained code snippet in a markdown code block.

You are given a 2D integer array tiles where tiles[i] = [li, ri] represents that every tile j in the range li <= j <= ri is colored white.
You are also given an integer carpetLen, the length of a single carpet that can be placed anywhere.
Return the maximum number of white tiles that can be covered by the carpet.
 
Please complete the following python code precisely:
```python
class Solution:
    def maximumWhiteTiles(self, tiles: List[List[int]], carpetLen: int) -> int:
```