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

You are given an n x n integer matrix grid.
Generate an integer matrix maxLocal of size (n - 2) x (n - 2) such that:

maxLocal[i][j] is equal to the largest value of the 3 x 3 matrix in grid centered around row i + 1 and column j + 1.

In other words, we want to find the largest value in every contiguous 3 x 3 matrix in grid.
Return the generated matrix.
 
Please complete the following python code precisely:
```python
class Solution:
    def largestLocal(self, grid: List[List[int]]) -> List[List[int]]:
```