# 1289. Minimum Falling Path Sum II

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

## Description

Given an `n x n` integer matrix `grid`, return *the minimum sum of a **falling path with non-zero shifts***.

A **falling path with non-zero shifts** is a choice of exactly one element from each row of `grid` such that no two elements chosen in adjacent rows are in the same column.

**Example 1:**

![](https://assets.leetcode.com/uploads/2021/08/10/falling-grid.jpg)

```
**Input:** arr = [[1,2,3],[4,5,6],[7,8,9]]
**Output:** 13
**Explanation:** 
The possible falling paths are:
[1,5,9], [1,5,7], [1,6,7], [1,6,8],
[2,4,8], [2,4,9], [2,6,7], [2,6,8],
[3,4,8], [3,4,9], [3,5,7], [3,5,9]
The falling path with the smallest sum is [1,5,7], so the answer is 13.
```

**Example 2:**

```
**Input:** grid = [[7]]
**Output:** 7
```

**Constraints:**

* `n == grid.length == grid[i].length`
* `1 <= n <= 200`
* `-99 <= grid[i][j] <= 99`

## ac

```java
```