Swapping Problem

Description:

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 $$$\sum_{i}|a_{i}-b_{i}|$$$.

Sample Input:

5
5 4 3 2 1
1 2 3 4 5

Sample Output:

4

Sample Input:

2
1 3
4 2

Sample Output:

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 $$$2$$$.