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

A rhombus shape within grid has its border formed by connecting four corners: $(r, c)$, $(r + k, c + k)$, $(r + 2 \cdot k, c)$, and $(r + k, c - k)$ for some non negative integer $k \ge 0$. If $k = 0$, the rhombus degenerates to a single cell located at $(r, c)$. All cells along the perimeter of the rhombus must strictly lie within the grid boundaries.

The rhombus sum is the sum of the elements residing on the border of the rhombus.

Return the $3$ largest distinct rhombus sums in descending order. If there are fewer than $3$ distinct rhombus sums, return all of them.

Constraints:

• m $==$ grid.length

• n $==$ grid[i].length

• $1 \le$ m, n $\le 50$

• $1 \le$ grid[i][j] $\le 10^5$

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.