<p>Given an <code>m x n</code> binary <code>matrix</code> filled with <code>0</code>&#39;s and <code>1</code>&#39;s, <em>find the largest square containing only</em> <code>1</code>&#39;s <em>and return its area</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/26/max1grid.jpg" style="width: 400px; height: 319px;" />
<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> 4
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/26/max2grid.jpg" style="width: 165px; height: 165px;" />
<pre>
<strong>Input:</strong> matrix = [[&quot;0&quot;,&quot;1&quot;],[&quot;1&quot;,&quot;0&quot;]]
<strong>Output:</strong> 1
</pre>

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

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

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

<ul>
	<li><code>m == matrix.length</code></li>
	<li><code>n == matrix[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 300</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 maximalSquare(self, matrix: List[List[str]]) -> int:
        m, n = len(matrix), len(matrix[0])
        f = [[[i, j] for j in range(n)] for i in range(m)]
        ans = 0
        for i in range(m):
            if matrix[i][0] == "1":
                ans = 1
        for j in range(n):
            if matrix[0][j] == "1":
                ans = 1
        for i in range(1, m):
            for j in range(1, n):
                if matrix[i][j] == "0":
                    continue
                ans = max(ans, 1)
                if matrix[i - 1][j - 1] == "1":
                    r, c = f[i - 1][j - 1]
                    new_r, new_c = r, c
                    flag = True
                    for col in range(c, j):
                        if matrix[i][col] == "0":
                            new_c = col + 1
                    for row in range(r, i):
                        if matrix[row][j] == "0":
                            new_r = row + 1
                    if i - new_r > j - new_c:
                        new_r = i - (j - new_c)
                    elif i - new_r < j - new_c:
                        new_c = j - (i - new_r)
                    if flag:
                        f[i][j] = [new_r, new_c]
                        ans = max(ans, (i - new_r + 1) * (j - new_c + 1))
        return ans
26725