Minimize Absolute Differences with Uniform Shift

You are given two arrays (A = [A_1, A_2, \dots, A_n]) and (B = [B_1, B_2, \dots, B_n]) of length (n). You are allowed to perform a uniform modification on array (B): choose an integer (x) (which may be positive, negative, or zero) and add it to every element of (B). After this operation, array (B) becomes (B' = [B_1+x, B_2+x, \dots, B_n+x]).

The goal is to choose (x) such that the sum of absolute differences [ S(x) = \sum_{i=1}^{n} \left| A_i - (B_i + x) \right| ] is minimized.

A well known fact in optimization is that the function (S(x)) is minimized when (x) is chosen so that it offsets the median of the differences (D_i = A_i - B_i). In other words, if you let (m) be the median of ({D_1, D_2, \dots, D_n}), then the minimum possible sum is [ S_{min} = \sum_{i=1}^{n} \left| D_i - m \right|. ]

Your task is to compute (S_{min}) given arrays (A) and (B).

inputFormat

The input is read from standard input (stdin) and consists of three lines:

1. The first line contains an integer (n) ((1 \le n \le 10^5)), the number of elements in each array.
2. The second line contains (n) space-separated integers representing array (A).
3. The third line contains (n) space-separated integers representing array (B).

outputFormat

Output to standard output (stdout) a single integer: the minimum possible sum of absolute differences after applying the optimal uniform modification to array (B).## sample

3
1 3 5
2 6 8

2