<p>Given an array of integers <code>heights</code> representing the histogram&#39;s bar height where the width of each bar is <code>1</code>, return <em>the area of the largest rectangle in the histogram</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/04/histogram.jpg" style="width: 522px; height: 242px;" />
<pre>
<strong>Input:</strong> heights = [2,1,5,6,2,3]
<strong>Output:</strong> 10
<strong>Explanation:</strong> The above is a histogram where width of each bar is 1.
The largest rectangle is shown in the red area, which has an area = 10 units.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/04/histogram-1.jpg" style="width: 202px; height: 362px;" />
<pre>
<strong>Input:</strong> heights = [2,4]
<strong>Output:</strong> 4
</pre>

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

<ul>
	<li><code>1 &lt;= heights.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= heights[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution:
    def largestRectangleArea(self, heights: List[int]) -> int:
        st = []
        n = len(heights)
        prevSm = [-1 for _ in range(n)]
        for i in range(n):
            while len(st) and st[-1][0] >= heights[i]:
                st.pop()
            if len(st):
                prevSm[i] = st[-1][1]
            st.append([heights[i], i])
        
        st = []
        nextSm = [n for _ in range(n)]
        for i in range(n-1, -1, -1):
            while len(st) and st[-1][0] >= heights[i]:
                st.pop()
            if len(st):
                nextSm[i] = st[-1][1]
            st.append([heights[i], i])
        
        maxA = 0
        for i in range(n):
            maxA = max(maxA, heights[i] * (nextSm[i] - prevSm[i] - 1))
        return maxA



        
27900