<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:
        counts = [[0 for i in range(len(matrix[0])+1)] for j in range(len(matrix)+1)]
        out = 0
        for i in range(len(matrix)):
            for j in range(len(matrix[0])):
                counts[i+1][j+1] += counts[i][j+1]
                counts[i+1][j+1] += counts[i+1][j]
                counts[i+1][j+1] -= counts[i][j]
                if matrix[i][j] == '1':
                    counts[i+1][j+1] += 1
        for i in range(len(matrix)):
            for j in range(len(matrix[0])):
                if matrix[i][j] == '1':
                    for x in range(i, len(matrix)):
                        if matrix[x][j] == '1':
                            l, r = j, len(matrix[0])-1
                            while l<=r:
                                y = (l+r)//2
                                if matrix[x][y] == '1':
                                    temp = counts[x+1][y+1] - counts[i][y+1] - counts[x+1][j] + counts[i][j]
                                    if temp == (x-i+1)*(y-j+1):
                                        out = max(out, temp)
                                        l = y+1
                                    else:
                                        r = y-1
                                else:
                                    r = y-1
                        else:
                            break

        return out




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