<p>A <code>k x k</code> <strong>magic square</strong> is a <code>k x k</code> grid filled with integers such that every row sum, every column sum, and both diagonal sums are <strong>all equal</strong>. The integers in the magic square <strong>do not have to be distinct</strong>. Every <code>1 x 1</code> grid is trivially a <strong>magic square</strong>.</p>

<p>Given an <code>m x n</code> integer <code>grid</code>, return <em>the <strong>size</strong> (i.e., the side length </em><code>k</code><em>) of the <strong>largest magic square</strong> that can be found within this grid</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/05/29/magicsquare-grid.jpg" style="width: 413px; height: 335px;" />
<pre>
<strong>Input:</strong> grid = [[7,1,4,5,6],[2,5,1,6,4],[1,5,4,3,2],[1,2,7,3,4]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The largest magic square has a size of 3.
Every row sum, column sum, and diagonal sum of this magic square is equal to 12.
- Row sums: 5+1+6 = 5+4+3 = 2+7+3 = 12
- Column sums: 5+5+2 = 1+4+7 = 6+3+3 = 12
- Diagonal sums: 5+4+3 = 6+4+2 = 12
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/05/29/magicsquare2-grid.jpg" style="width: 333px; height: 255px;" />
<pre>
<strong>Input:</strong> grid = [[5,1,3,1],[9,3,3,1],[1,3,3,8]]
<strong>Output:</strong> 2
</pre>

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

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 50</code></li>
	<li><code>1 &lt;= grid[i][j] &lt;= 10<sup>6</sup></code></li>
</ul>

class Solution:
    def largestMagicSquare(self, grid: List[List[int]]) -> int:
        rows = len(grid)
        cols = len(grid[0])
        max_k = min(rows,cols)
        res = 1


        def magic_square(r,c,k):    
            target = sum(grid[r][c:c+k])
            # Calculation of row_sum
            for i in range(r,r+k):
                row_sum = sum(grid[i][c:c+k])
             
                if row_sum != target:
                    return False
            

            # Calculation of col_sum
            for i in range(c,c+k):
                col_sum = 0
                for j in range(r,r+k):
                    col_sum += grid[j][i]

                if col_sum != target:
                    return False
            
            # Calculation of diagonal sums

            pos_diag = sum(grid[r + i][c + i] for i in range(k))
            neg_diag = sum(grid[r + i][c + k - 1 - i] for i in range(k))

            if pos_diag != target or neg_diag != target:
                return False
            return True

        for r in range(rows):
            for c in range(cols):
                for k in range(2,max_k+1):
                    # if r == 1 and c == 1:
                        # print(r," ",c," ",k)
                    if (r+k) in range(rows+1) and (c+k) in range(cols+1):
                        if magic_square(r,c,k):
                            
                            # print("hello")
                            res = max(res,k)
        return res
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