<p>Given a <code>rows x cols</code>&nbsp;binary <code>matrix</code> filled with <code>0</code>&#39;s and <code>1</code>&#39;s, find the largest rectangle containing only <code>1</code>&#39;s and return <em>its area</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/14/maximal.jpg" style="width: 402px; height: 322px;" />
<pre>
<strong>Input:</strong> matrix = [[&quot;1&quot;,&quot;0&quot;,&quot;1&quot;,&quot;0&quot;,&quot;0&quot;],[&quot;1&quot;,&quot;0&quot;,&quot;1&quot;,&quot;1&quot;,&quot;1&quot;],[&quot;1&quot;,&quot;1&quot;,&quot;1&quot;,&quot;1&quot;,&quot;1&quot;],[&quot;1&quot;,&quot;0&quot;,&quot;0&quot;,&quot;1&quot;,&quot;0&quot;]]
<strong>Output:</strong> 6
<strong>Explanation:</strong> The maximal rectangle is shown in the above picture.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> matrix = [[&quot;0&quot;]]
<strong>Output:</strong> 0
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> matrix = [[&quot;1&quot;]]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>rows == matrix.length</code></li>
	<li><code>cols == matrix[i].length</code></li>
	<li><code>1 &lt;= row, cols &lt;= 200</code></li>
	<li><code>matrix[i][j]</code> is <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>
</ul>

class Solution:
    def maximalRectangle(self, matrix: List[List[str]]) -> int:
        def maxArea(heights):
            n = len(heights)
            left = list(range(n))
            right = list(range(n))

            # to right
            stack = []
            for i in range(n):
                cur = heights[i]
                if len(stack) == 0 or cur >= stack[-1][1]:
                    stack.append((i, cur))
                else:
                    while stack and cur < stack[-1][1]:
                        top = stack.pop()
                        right[top[0]] = i
                    stack.append((i, cur))
            while stack:
                top = stack.pop()
                right[top[0]] = n
            # to left
            for i in range(n-1, -1, -1):
                cur = heights[i]
                if len(stack) == 0 or cur >= stack[-1][1]:
                    stack.append((i, cur))
                else:
                    while stack and cur < stack[-1][1]:
                        top = stack.pop()
                        left[top[0]] = i
                    stack.append((i, cur))
            while stack:
                top = stack.pop()
                left[top[0]] = -1
             
            max_val = -1
            for i in range(n):
                s = left[i]
                e = right[i]
                h = heights[i]
                v = (e - s - 1) * h
                if max_val < v:
                    max_val = v
            
            return max_val

        n = len(matrix)
        m = len(matrix[0])
        heights = [0] * m
        max_val = 0
        for i in range(n):
            for j in range(m):
                if matrix[i][j] == "0":
                    heights[j] = 0
                else:
                    heights[j] += int(matrix[i][j])
            val = maxArea(heights)
            if val > max_val:
                max_val = val
        
        return max_val

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