Swapping Problem
Description
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 $\sum_{i}|a_{i}-b_{i}|$.
Input
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
Output the minimum value of $\sum_{i}|a_{i}-b_{i}|$.
Samples
5
5 4 3 2 1
1 2 3 4 5
4
2
1 3
4 2
2
Note
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 $2$.