<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:
        
            max_area: int = 0 # 7 
            stack: list[(int, int)] = [] # (1, 0), (3, 1)

            for i, height in enumerate(heights): # 0, 1 | 1, 3 | 3, 2
                if not stack:  # the stack is empty
                    stack.append((height, i))
                    continue

                start = i
                while stack and height < stack[-1][0]:
                    rect_height, start = stack.pop()
                    rect_area = rect_height * (i - start)
                    max_area = max(max_area, rect_area)
            
                stack.append((height, start))
                
            while stack: # [1, 0 | 2, 3]
                rect_height, start = stack.pop()
                rect_area = rect_height * (len(heights) - start)
                print(rect_height, start, rect_area)
                max_area = max(max_area, rect_area)

            return max_area
        
34200