<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:

        def ngl(nums):
            n=len(nums)
            stack=[]
            res=[]

            for i in range(n):
          
                if len(stack)==0:
                    res.append(-1)
                elif len(stack)>0 and stack[-1][1]<nums[i]:
                    res.append(stack[-1][0])
                elif len(stack)>0 and stack[-1][1]>=nums[i]:
                    while len(stack)>0 and stack[-1][1]>=nums[i]:
                        stack.pop()
                    if len(stack)==0:
                        res.append(-1)
                    else:
                        res.append(stack[-1][0])
                stack.append([i,nums[i]])
            return(res)

        def ngr(nums):
            nums.append(-1)
            n=len(nums)
            stack=[]
            res=[]

            for i in range(n-1,-1,-1):

                if len(stack)==0:
                    res.append(-1)
                elif len(stack)>0 and stack[-1][1]<nums[i]:
                    res.append(stack[-1][0])
                elif len(stack)>0 and stack[-1][1]>=nums[i]:
                    while len(stack)>0 and stack[-1][1]>=nums[i]:
                        stack.pop()
                    if len(stack)==0:
                        res.append(-1)
                    else:
                        res.append(stack[-1][0])
                stack.append([i,nums[i]])
            return(res[::-1])

        a=(ngl(heights))
        b=(ngr(heights))
        c=[]
        n=len(a)
        for i in range(n):
            c.append((b[i]-a[i]-1)*heights[i])
        return(max(c))

  
        
31700