You are given an array heights of n integers representing the number of bricks in n consecutive towers. Your task is to remove some bricks to form a mountain-shaped tower arrangement. In this arrangement, the tower heights are non-decreasing, reaching a maximum peak value with one or multiple consecutive towers and then non-increasing.
Return the maximum possible sum of heights of a mountain-shaped tower arrangement.
Example 1:
Input: heights = [5,3,4,1,1]
Output: 13
Explanation:
We remove some bricks to make heights = [5,3,3,1,1], the peak is at index 0.
Example 2:
Input: heights = [6,5,3,9,2,7]
Output: 22
Explanation:
We remove some bricks to make heights = [3,3,3,9,2,2], the peak is at index 3.
Example 3:
Input: heights = [3,2,5,5,2,3]
Output: 18
Explanation:
We remove some bricks to make heights = [2,2,5,5,2,2], the peak is at index 2 or 3.
Constraints:
1 <= n == heights.length <= 1031 <= heights[i] <= 109