<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:
    "to katw dexia kanei define"
    def maximalSquare(self, matrix: List[List[str]]) -> int:
        m = len(matrix)
        n = len(matrix[0])
        res = [[0 for _ in range(n)] for _ in range(m)]
        test = [[[0,0] for _ in range(n)] for _ in range(m)]
        
        for row in range(m):
            for col in range(n):
                matrix[row][col] = int(matrix[row][col])
        for col in range(1, n):
            test[0][col][0] = (1+test[0][col-1][0]) * matrix[0][col-1]
        for row in range(1, m):
            test[row][0][1] = (1+test[row-1][0][1]) * matrix[row-1][0]
        for row in range(1, m):
            for col in range(1, n):
                test[row][col][0] = (1+test[row][col-1][0]) * matrix[row][col-1]
                test[row][col][1] = (1+test[row-1][col][1]) * matrix[row-1][col]
                
        for row in range(m):
            for col in range(n):
                res[row][col] = int(matrix[row][col])
                for size in reversed(range(2, min(row+2, col+2))):
                    if matrix[row][col] == 1 and res[row-1][col-1] >= size-1 and min(test[row][col]) >= size-1: 
                        res[row][col] = size
                        break
    
        max_size = max([max(i) for i in res])
        return max_size**2




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