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

You are given an integer array nums of size n. You are asked to solve n queries for each integer i in the range 0 <= i < n.
To solve the ith query:

Find the minimum value in each possible subarray of size i + 1 of the array nums.
Find the maximum of those minimum values. This maximum is the answer to the query.

Return a 0-indexed integer array ans of size n such that ans[i] is the answer to the ith query.
A subarray is a contiguous sequence of elements in an array.
 
Please complete the following python code precisely:
```python
class Solution:
    def findMaximums(self, nums: List[int]) -> List[int]:
```