# 1671. Minimum Number of Removals to Make Mountain Array

<https://leetcode.com/problems/minimum-number-of-removals-to-make-mountain-array>

## Description

You may recall that an array `arr` is a **mountain array** if and only if:

* `arr.length >= 3`
* There exists some index `i` (**0-indexed**) with `0 < i < arr.length - 1` such that:
  * `arr[0] < arr[1] < ... < arr[i - 1] < arr[i]`
  * `arr[i] > arr[i + 1] > ... > arr[arr.length - 1]`

Given an integer array `nums`​​​, return *the **minimum** number of elements to remove to make* `nums*​​​*`*a **mountain array**.*

**Example 1:**

```
**Input:** nums = [1,3,1]
**Output:** 0
**Explanation:** The array itself is a mountain array so we do not need to remove any elements.
```

**Example 2:**

```
**Input:** nums = [2,1,1,5,6,2,3,1]
**Output:** 3
**Explanation:** One solution is to remove the elements at indices 0, 1, and 5, making the array nums = [1,5,6,3,1].
```

**Example 3:**

```
**Input:** nums = [4,3,2,1,1,2,3,1]
**Output:** 4
```

**Example 4:**

```
**Input:** nums = [1,2,3,4,4,3,2,1]
**Output:** 1
```

**Constraints:**

* `3 <= nums.length <= 1000`
* `1 <= nums[i] <= 109`
* It is guaranteed that you can make a mountain array out of `nums`.

## ac

```java
```


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