<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>

from collections import deque
class Solution:
    def maximumSumOfHeights(self, h: List[int]) -> int:
        le = len(h)
        stack = deque([(h[0],1)])
        r = [0]*le
        l = r.copy()
        
        l[0] = h[0]
        r[-1] = h[-1]


        for i in range(1,le):
            curr = h[i]
            s = l[i-1] + curr
            times = 1
            while stack and stack[-1][0] >= curr:
                s_top = stack.pop()
                s += (-s_top[0] + curr)*s_top[1]
                times += s_top[1]

            stack.append( (curr,times ))
            
            l[i]=s

        stack = deque([(h[-1],1)])

        for i in range(le-2, -1, -1):
            curr = h[i]
            s = r[i+1] + curr
            times = 1
            while stack and stack[-1][0] >= curr:
                s_top = stack.pop()
                s += (-s_top[0] + curr)*s_top[1]
                times += s_top[1]

            stack.append( (curr,times ))
            
            r[i]=s


        return max( r[i] + l[i] - h[i] for i in range(le))
        return 3



        
17000