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

A matrix diagonal is a diagonal line of cells starting from some cell in either the topmost row or leftmost column and going in the bottom-right direction until reaching the matrix's end. For example, the matrix diagonal starting from mat[2][0], where mat is a 6 x 3 matrix, includes cells mat[2][0], mat[3][1], and mat[4][2].
Given an m x n matrix mat of integers, sort each matrix diagonal in ascending order and return the resulting matrix.
 
Please complete the following python code precisely:
```python
class Solution:
    def diagonalSort(self, mat: List[List[int]]) -> List[List[int]]:
```