Minimum Number of Removals to Make Mountain Array

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

  #
  #
# # #
1 3 1

Inputnums = [1,3,1]

Output0

The array itself is a mountain array so we do not need to remove any elements.

Example 2

        #
      # #
      # #
      # #   #
#     # # # #
# # # # # # # #
2 1 1 5 6 2 3 1

Inputnums = [2,1,1,5,6,2,3,1]

Output3

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

Constraints