<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:
        ROWS = len(matrix)
        COLS = len(matrix[0])
        for r in range(ROWS):
            for c in range(COLS):
                matrix[r][c] = int(matrix[r][c])
        prefix = [[0] * (COLS + 1) for _ in range(ROWS + 1)]
        for r in range(1, ROWS+1):
            for c in range(1, COLS+1):
                prefix[r][c] = matrix[r-1][c-1] + prefix[r-1][c] + prefix[r][c-1] - prefix[r-1][c-1]
        
        def is_rectange(start, end):
            r_start, c_start = start
            r_end, c_end = end
            area = prefix[r_end+1][c_end+1] + prefix[r_start][c_start] - prefix[r_start][c_end+1] - prefix[r_end+1][c_start]
            is_rectangle = area == (r_end - r_start + 1) * (c_end - c_start + 1)
            return is_rectangle
        
        def get_area(start, end):
            r_start, c_start = start
            r_end, c_end = end
            return (r_end - r_start + 1) * (c_end - c_start + 1)

        max_area = 0
        for start_row in range(ROWS):
            for end_row in range(start_row, ROWS):
                cur = 0
                for i in range(COLS):
                    if is_rectange((start_row, i), (end_row, i)):
                        cur += get_area((start_row, i), (end_row, i))
                        max_area = max(max_area, cur)
                    else:
                        cur = 0
        return max_area
18600