# 1818. Minimum Absolute Sum Difference

<https://leetcode.com/problems/minimum-absolute-sum-difference>

## Description

You are given two positive integer arrays `nums1` and `nums2`, both of length `n`.

The **absolute sum difference** of arrays `nums1` and `nums2` is defined as the **sum** of `|nums1[i] - nums2[i]|` for each `0 <= i < n` (**0-indexed**).

You can replace **at most one** element of `nums1` with **any** other element in `nums1` to **minimize** the absolute sum difference.

Return the *minimum absolute sum difference **after** replacing at most oneelement in the array `nums1`.* Since the answer may be large, return it **modulo** `109 + 7`.

`|x|` is defined as:

* `x` if `x >= 0`, or
* `-x` if `x < 0`.

**Example 1:**

```
**Input:** nums1 = [1,7,5], nums2 = [2,3,5]
**Output:** 3
**Explanation:** There are two possible optimal solutions:
- Replace the second element with the first: [1,**7**,5] => [1,**1**,5], or
- Replace the second element with the third: [1,**7**,5] => [1,**5**,5].
Both will yield an absolute sum difference of |1-2| + (|1-3| or |5-3|) + |5-5| = 3.
```

**Example 2:**

```
**Input:** nums1 = [2,4,6,8,10], nums2 = [2,4,6,8,10]
**Output:** 0
**Explanation:** nums1 is equal to nums2 so no replacement is needed. This will result in an 
absolute sum difference of 0.
```

**Example 3:**

```
**Input:** nums1 = [1,10,4,4,2,7], nums2 = [9,3,5,1,7,4]
**Output:** 20
**Explanation:** Replace the first element with the second: [**1**,10,4,4,2,7] => [**10**,10,4,4,2,7].
This yields an absolute sum difference of |10-9| + |10-3| + |4-5| + |4-1| + |2-7| + |7-4| = 20
```

**Constraints:**

* `n == nums1.length`
* `n == nums2.length`
* `1 <= n <= 105`
* `1 <= nums1[i], nums2[i] <= 105`

## ac

```java
```