1671. Minimum Number of Removals to Make Mountain Array

Hard

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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`**

**Example 1:**

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

**Constraints:**

`3 <= nums.length <= 1000`

`1 <= nums[i] <= 10`

^{9}- It is guaranteed that you can make a mountain array out of
`nums`

.

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