An array arr is defined as a mountain array if and only if:

• arr.length $\geq 3$

• There exists some index i with $0 < i <$ arr.length $- 1$ such that:

  • arr[0] < arr[1] < $\dots$ < arr[i - 1] < arr[i]

  • arr[i] > arr[i + 1] > $\dots$ > arr[arr.length - 1]

Given an integer array nums, return the minimum number of elements that must be removed to make nums a mountain array.

Constraints:

• $3 \leq$ nums.length $\leq 1000$

• $1 \leq$ nums[i] $\leq 10^9$

• It is guaranteed that you can make a mountain array out of nums.

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