<p>You are given an array <code>heights</code> of <code>n</code> integers representing the number of bricks in <code>n</code> consecutive towers. Your task is to remove some bricks to form a <strong>mountain-shaped</strong> 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.</p>

<p>Return the <strong>maximum possible sum</strong> of heights of a mountain-shaped tower arrangement.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">heights = [5,3,4,1,1]</span></p>

<p><strong>Output:</strong> <span class="example-io">13</span></p>

<p><strong>Explanation:</strong></p>

<p>We remove some bricks to make <code>heights =&nbsp;[5,3,3,1,1]</code>, the peak is at index 0.</p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">heights = [6,5,3,9,2,7]</span></p>

<p><strong>Output:</strong> <span class="example-io">22</span></p>

<p><strong>Explanation:</strong></p>

<p>We remove some bricks to make <code>heights =&nbsp;[3,3,3,9,2,2]</code>, the peak is at index 3.</p>
</div>

<p><strong class="example">Example 3:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">heights = [3,2,5,5,2,3]</span></p>

<p><strong>Output:</strong> <span class="example-io">18</span></p>

<p><strong>Explanation:</strong></p>

<p>We remove some bricks to make <code>heights = [2,2,5,5,2,2]</code>, the peak is at index 2 or 3.</p>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n == heights.length &lt;= 10<sup>3</sup></code></li>
	<li><code>1 &lt;= heights[i] &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
    def maximumSumOfHeights(self, maxHeights: List[int]) -> int:
        # https://github.com/doocs/leetcode/tree/main/solution/2800-2899/2865.Beautiful%20Towers%20I
        n = len(maxHeights)
        ans = 0        
        for i in range(n):
            heights = [0] * n
            heights[i] = maxHeights[i]
            cur = maxHeights[i]
            if i > 0:
                for j in range(i - 1, -1, -1):
                    heights[j] = min(maxHeights[j], heights[j + 1])
                    cur += heights[j]
            if i < n - 1:
                for j in range(i + 1, n):
                    heights[j] = min(maxHeights[j], heights[j - 1])
                    cur += heights[j]
            ans = max(ans, cur)
        return ans

        # n = len(maxHeights)
        # prefix = [float(inf)] * n
        # postfix = [float(inf)] * n
        # prefix[0] = maxHeights[0]
        # cur = maxHeights[0]
        # for i, h in enumerate(1, maxHeights):
        #     prefix[i] = min(prefix(i-1), h)
        # postfix[-1] = maxHeight[-1]
        # for i in range(n-2, -1, -1):
        #     postfix[i] = min(postfix[i+1], maxHeights[i])
        # ans = 0
        # for i in range(n):
        #     if i == 0:
        #         cur = postfix[i-1]


1615