A14211. Swapping Problem

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.

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 $b_1, b_2, \ldots, b_n$ ( $1 \le b_i \le {10^9}$ ).

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

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 $2$ .