<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:
        m, n = len(grid), len(grid[0])

        cumrow = [[0] * (n+1) for _ in range(m)]
        for i in range(m):
            for j in range(n):
                cumrow[i][j+1] = cumrow[i][j] + grid[i][j]
        cumcol = [[0] * n for _ in range(m+1)]
        for j in range(n):
            for i in range(m):
                cumcol[i+1][j] = cumcol[i][j] + grid[i][j]
        # print("cumrow", cumrow)
        # print("cumcol", cumcol)

        for k in range(min(m, n), 1, -1):
            for i0 in range(m-k+1):
                for j0 in range(n-k+1):
                    soms = {cumrow[i][j0+k] - cumrow[i][j0] for i in range(i0, i0+k)}
                    for j in range(j0, j0+k):
                        soms.add(cumcol[i0+k][j] - cumcol[i0][j])
                    soms.add(sum(grid[i0+d][j0+d] for d in range(k)))
                    soms.add(sum(grid[i0+k-1-d][j0+d] for d in range(k)))
                    if len(soms) == 1:
                        return k
                    # print("fuck", k, [[grid[i][j] for j in range(j0, j0+k)] for i in range(i0, i0+k)], soms)

        return 1
835