F. Swapping Problemtime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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}).OutputOutput the minimum value of \sum_{i}|a_{i}-b_{i}|.ExamplesInput
5
5 4 3 2 1
1 2 3 4 5
Output
4Input
2
1 3
4 2
Output
2NoteIn 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.
5
5 4 3 2 1
1 2 3 4 5

4
['brute force', 'constructive algorithms', 'data structures', 'sortings', '*2500']