<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:
    @staticmethod
    def mrec(matrix: List[List[str]], k, l, mms):
        n = len(matrix)
        m = len(matrix[0])
        ms = mms
        pj = m
        i = k
        if (n - k) * (pj - l) <= ms:
            return ms
        while i < n:
            if (n - k) * (pj - l) <= ms:
                break
            j = l
            while j < pj:
                if matrix[i][j] == '0':
                    break
                j += 1
            s = (i - k + 1) * (j - l)
            if s > ms:
                ms = s
            pj = j
            i += 1
        return ms

    def maximalRectangle(self, matrix: List[List[str]]) -> int:
        n = len(matrix)
        m = 0 if n == 0 else len(matrix[0])
        ms = 0
        for i in range(n):
            for j in range(m):
                # if ((n - i) * (m - j)) < ms:
                #     break
                s = self.mrec(matrix, i, j, ms)
                if s > ms:
                    ms = s
        return ms

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