# 0931. Minimum Falling Path Sum

<https://leetcode.com/problems/minimum-falling-path-sum>

## Description

Given an `n x n` array of integers `matrix`, return *the **minimum sum** of any **falling path** through* `matrix`.

A **falling path** starts at any element in the first row and chooses the element in the next row that is either directly below or diagonally left/right. Specifically, the next element from position `(row, col)` will be `(row + 1, col - 1)`, `(row + 1, col)`, or `(row + 1, col + 1)`.

**Example 1:**

```
**Input:** matrix = [[2,1,3],[6,5,4],[7,8,9]]
**Output:** 13
**Explanation:** There are two falling paths with a minimum sum underlined below:
[[2,1,3],      [[2,1,3],
 [6,5,4],       [6,5,4],
 [7,8,9]]       [7,8,9]]
```

**Example 2:**

```
**Input:** matrix = [[-19,57],[-40,-5]]
**Output:** -59
**Explanation:** The falling path with a minimum sum is underlined below:
[[-19,57],
 [-40,-5]]
```

**Example 3:**

```
**Input:** matrix = [[-48]]
**Output:** -48
```

**Constraints:**

* `n == matrix.length`
* `n == matrix[i].length`
* `1 <= n <= 100`
* `-100 <= matrix[i][j] <= 100`

## ac

```java
```