<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:
        
        nrow = len(grid)
        ncol = len(grid[0])

        if nrow == 1 or ncol == 1:
            return 1

        size = min(nrow, ncol)
        while size >= 1:

            r1 = 0
            r2 = size - 1

            while r2 < nrow:

                pointers = [p for p in range(size)]

                while pointers[-1] < ncol:

                    memory = []
                    for r in range(r1, r2 + 1):
                        current = []
                        for p in pointers:
                            current.append(grid[r][p])
                        memory.append(current)

                    values = []
                    p1 = 0
                    p2 = size - 1
                    rdvalue = 0
                    dvalue = 0
                    for i in range(size):

                        rvalue = 0
                        cvalue = 0

                        for j in range(size):

                            if i == j:
                                dvalue += memory[i][j]

                            rvalue += memory[i][j]
                            cvalue += memory[j][i]

                        values.extend([rvalue, cvalue])

                        rdvalue += memory[p1][p2]
                        p1 += 1
                        p2 -= 1

                    values.extend([dvalue, rdvalue])

                    new_pointers = []
                    for p in pointers:
                        new_pointers.append(p + 1)
                    pointers = new_pointers

                    gate = True
                    current = 0
                    for value in values:
                        if current == 0:
                            current = value
                        elif value != current:
                            gate = False
                            break
                    if gate:
                        return size
                    # print(values, pointers)
                
                r1 += 1
                r2 += 1

            size -= 1
4359