<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:
        row = len(matrix)
        col = len(matrix[0])
        tab = [ [0 for _ in range(col)] for _ in range(row)]

        def largestRectangleArea(heights: List[int]) -> int:
            n = len(heights)
            stk = [] 
            maxx = 0

            for i in range(n):
                start = i
                while stk and heights[i]<stk[-1][1]:
                    maxx = max(maxx, stk[-1][1]*( i - stk[-1][0]) ) 
                    start=stk.pop()[0]
                stk.append([start, heights[i]])
            
            while stk:
                maxx= max(maxx, stk[-1][1]*( n - stk[-1][0]))
                stk.pop()
            return maxx

        for i in range(col):
            if matrix[0][i]=='0':
                tab[0][i]=0
            else:
                tab[0][i]=1
        
        maxx2 = largestRectangleArea(tab[0])
        
        for i in range(1,row):
            for j in range(col):
                if matrix[i][j]=='0':
                    tab[i][j] = 0
                else:
                    tab[i][j] = 1 + tab[i-1][j]
                maxx2 = max(maxx2, largestRectangleArea(tab[i]))
        return maxx2
                
        
18100