1895. Largest Magic Square

class Solution:
    def largestMagicSquare(self, grid: List[List[int]]) -> int:
        m, n = len(grid), len(grid[0])
        rowsum = [[0] * (n + 1) for _ in range(m + 1)]
        colsum = [[0] * (n + 1) for _ in range(m + 1)]
        for i in range(1, m + 1):
            for j in range(1, n + 1):
                rowsum[i][j] = rowsum[i][j - 1] + grid[i - 1][j - 1]
                colsum[i][j] = colsum[i - 1][j] + grid[i - 1][j - 1]

        def check(x1, y1, x2, y2):
            val = rowsum[x1 + 1][y2 + 1] - rowsum[x1 + 1][y1]
            for i in range(x1 + 1, x2 + 1):
                if rowsum[i + 1][y2 + 1] - rowsum[i + 1][y1] != val:
                    return False
            for j in range(y1, y2 + 1):
                if colsum[x2 + 1][j + 1] - colsum[x1][j + 1] != val:
                    return False
            s, i, j = 0, x1, y1
            while i <= x2:
                s += grid[i][j]
                i += 1
                j += 1
            if s != val:
                return False
            s, i, j = 0, x1, y2
            while i <= x2:
                s += grid[i][j]
                i += 1
                j -= 1
            if s != val:
                return False
            return True

        for k in range(min(m, n), 1, -1):
            i = 0
            while i + k - 1 < m:
                j = 0
                while j + k - 1 < n:
                    i2, j2 = i + k - 1, j + k - 1
                    if check(i, j, i2, j2):
                        return k
                    j += 1
                i += 1
        return 1