<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>

from dataclasses import dataclass
@dataclass
class Cell:
    # right_ones: int = 0
    # down_ones: int = 0 
    square_size: int = 0

class Solution:
    def maximalSquare(self, matrix: List[List[str]]) -> int:

        rows_num = len(matrix)
        cols_num = len(matrix[0])
        cells = [[Cell() for _ in range(cols_num + 1)]
                     for _ in range(rows_num + 1)]

        def print_cells(cells, cur_row, cur_col):
            for row in range(len(cells) - 1):
                print()
                for col in range(len(cells[0]) - 1):
                    c = cells[row][col]
                    mark = '*' if cur_col == col and cur_row == row else '('
                    print(f'{mark}{c.square_size}, {c.down_ones}, {c.right_ones})', end = ', ')

        max_square = 0
        for row in reversed(range(rows_num)):
            for col in reversed(range(cols_num)):
                if matrix[row][col] == "0":
                    continue
                cell = cells[row][col]
                right = cells[row][col + 1]
                down = cells[row + 1][col]
                diag = cells[row + 1][col + 1]
                # cell.right_ones = right.right_ones + 1
                # cell.down_ones = down.down_ones + 1

                # cell.square_size = min(diag.square_size, right.right_ones, down.down_ones) + 1
                cell.square_size = min(diag.square_size, right.square_size, down.square_size) + 1
                # if diag.square_size <= right.right_ones and diag.square_size <= down.down_ones:
                #     cell.square_size = diag.square_size + 1
                max_square = max(max_square, cell.square_size)
                # print(f'{row},{col}: {cell}, {matrix[row][col]}')
                # print_cells(cells, row, col)
                # print()
        # print(cells)
        
        return max_square * max_square


        
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