CF1513F.Swapping Problem

普及/提高-

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题目描述

You are given 2 arrays $a$ and $b$ , both of size $n$ . You can swap two elements in $b$ at most once (or leave it as it is), and you are required to minimize the value $$$$\sum_{i}|a_{i}-b_{i}|. $$$$

Find the minimum possible value of this sum.

输入格式

The first line contains a single integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ).

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le {10^9}$ ).

The third line contains $n$ integers $b_1, b_2, \ldots, b_n$ ( $1 \le b_i \le {10^9}$ ).

输出格式

Output the minimum value of $\sum_{i}|a_{i}-b_{i}|$ .

输入输出样例

输入#1
```
5
5 4 3 2 1
1 2 3 4 5
```
输出#1
```
4
```
输入#2
```
2
1 3
4 2
```
输出#2
```
2
```

说明/提示

In the first example, we can swap the first and fifth element in array $b$ , so that it becomes $[ 5, 2, 3, 4, 1 ]$ .

Therefore, the minimum possible value of this sum would be $|5-5| + |4-2| + |3-3| + |2-4| + |1-1| = 4$ .

In the second example, we can swap the first and second elements. So, our answer would be $2$ .

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