<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:
        res = 0


        for i in range(0 , len(maxHeights)):
    
            left = maxHeights[:i][::-1]
            right = maxHeights[i+1:]
    
    
            cur = maxHeights[i]
    
            l = 0
            for x in range(0,len(left)):
                if left[x] > cur:
                    l+=cur
                else:
                    l+=left[x]
            
                cur = min(cur , left[x])
        
            cur = maxHeights[i]
            r = 0
            for x in range(0,len(right)):
                if right[x] > cur:
                    r+=cur
                else:
                    r+=right[x]
            
                cur = min(cur , right[x])
        
        
            res = max(res , l+r+maxHeights[i])
    
    
        return(res)
            
            
        
    
    
        
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