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# 1950. Maximum of Minimum Values in All Subarrays

<https://leetcode.com/problems/maximum-of-minimum-values-in-all-subarrays>

## Description

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:

1. Find the **minimum value** in each possible subarray of size `i + 1` of the array `nums`.
2. 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.

**Example 1:**

```
**Input:** nums = [0,1,2,4]
**Output:** [4,2,1,0]
**Explanation:**
i=0:
- The subarrays of size 1 are [0], [1], [2], [4]. The minimum values are 0, 1, 2, 4.
- The maximum of the minimum values is 4.
i=1:
- The subarrays of size 2 are [0,1], [1,2], [2,4]. The minimum values are 0, 1, 2.
- The maximum of the minimum values is 2.
i=2:
- The subarrays of size 3 are [0,1,2], [1,2,4]. The minimum values are 0, 1.
- The maximum of the minimum values is 1.
i=3:
- There is one subarray of size 4, which is [0,1,2,4]. The minimum value is 0.
- There is only one value, so the maximum is 0.
```

**Example 2:**

```
**Input:** nums = [10,20,50,10]
**Output:** [50,20,10,10]
**Explanation:**
i=0:
- The subarrays of size 1 are [10], [20], [50], [10]. The minimum values are 10, 20, 50, 10.
- The maximum of the minimum values is 50.
i=1:
- The subarrays of size 2 are [10,20], [20,50], [50,10]. The minimum values are 10, 20, 10.
- The maximum of the minimum values is 20.
i=2:
- The subarrays of size 3 are [10,20,50], [20,50,10]. The minimum values are 10, 10.
- The maximum of the minimum values is 10.
i=3:
- There is one subarray of size 4, which is [10,20,50,10]. The minimum value is 10.
- There is only one value, so the maximum is 10.
```

**Constraints:**

* `n == nums.length`
* `1 <= n <= 105`
* `0 <= nums[i] <= 109`

## ac

```java
```