<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 getMaxSumWithPeak(self, heights: List[int], peak_i: int) -> int:
        max_sum = 0
        before_peak = heights[:peak_i + 1]
        for i in range(len(before_peak) - 2, -1, -1):
            if before_peak[i] > before_peak[i + 1]:
                before_peak[i] = before_peak[i + 1]
            max_sum += before_peak[i]

        max_sum += heights[peak_i]

        after_peak = heights[peak_i:]
        for dec_i in range(1, len(heights) - peak_i):
            if after_peak[dec_i] > after_peak[dec_i - 1]:
                after_peak[dec_i] = after_peak[dec_i - 1]
            max_sum += after_peak[dec_i]

        return max_sum

    def maximumSumOfHeights(self, heights: List[int]) -> int:
        max_sum = 0
        for i in range(len(heights)):
            sum_with_peak = self.getMaxSumWithPeak(heights, i)
            max_sum = max(max_sum, self.getMaxSumWithPeak(heights, i))

        return max_sum
        
1828