# 1878. Get Biggest Three Rhombus Sums in a Grid

https://leetcode.com/problems/get-biggest-three-rhombus-sums-in-a-grid

## Description

You are given an `m x n` integer matrix `grid`​​​.

A **rhombus sum** is the sum of the elements that form **the** **border** of a regular rhombus shape in `grid`​​​. The rhombus must have the shape of a square rotated 45 degrees with each of the corners centered in a grid cell. Below is an image of four valid rhombus shapes with the corresponding colored cells that should be included in each **rhombus sum**:

![](https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-desc-2.png) Note that the rhombus can have an area of 0, which is depicted by the purple rhombus in the bottom right corner.

Return _the biggest three **distinct rhombus sums** in the_ `grid` _in **descending order**_\*. If there are less than three distinct values, return all of them\*.

**Example 1:**

![](https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-ex1.png)

```
**Input:** grid = [[3,4,5,1,3],[3,3,4,2,3],[20,30,200,40,10],[1,5,5,4,1],[4,3,2,2,5]]
**Output:** [228,216,211]
**Explanation:** The rhombus shapes for the three biggest distinct rhombus sums are depicted above.
- Blue: 20 + 3 + 200 + 5 = 228
- Red: 200 + 2 + 10 + 4 = 216
- Green: 5 + 200 + 4 + 2 = 211
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-ex2.png)

```
**Input:** grid = [[1,2,3],[4,5,6],[7,8,9]]
**Output:** [20,9,8]
**Explanation:** The rhombus shapes for the three biggest distinct rhombus sums are depicted above.
- Blue: 4 + 2 + 6 + 8 = 20
- Red: 9 (area 0 rhombus in the bottom right corner)
- Green: 8 (area 0 rhombus in the bottom middle)
```

**Example 3:**

```
**Input:** grid = [[7,7,7]]
**Output:** [7]
**Explanation:** All three possible rhombus sums are the same, so return [7].
```

**Constraints:**

* `m == grid.length`
* `n == grid[i].length`
* `1 <= m, n <= 50`
* `1 <= grid[i][j] <= 105`

## ac

```java
```
