You are given an m $\times$ n integer matrix grid.

An hourglass is defined as a subset of elements from grid forming the following structure:
grid[r][c], grid[r][c + 1], grid[r][c + 2]
grid[r + 1][c + 1]
grid[r + 2][c], grid[r + 2][c + 1], grid[r + 2][c + 2]

Return the maximum sum of elements among all valid hourglasses in grid.

Note: An hourglass cannot be rotated and must be fully contained within the grid boundaries.

Constraints:

• m == grid.length

• n == grid[i].length

• $3 \leq$ m, n $\leq 150$

• $0 \leq$ grid[i][j] $\leq 10^6$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.