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

Given a 0-indexed integer array nums of size n containing all numbers from 1 to n, return the number of increasing quadruplets.
A quadruplet (i, j, k, l) is increasing if:

0 <= i < j < k < l < n, and
nums[i] < nums[k] < nums[j] < nums[l].

 
Please complete the following python code precisely:
```python
class Solution:
    def countQuadruplets(self, nums: List[int]) -> int:
```