Amazon Security Analysis (Min Distance Matching)

Match n centers with n destinations one-to-one; each pair costs the absolute difference of their coordinates. Find the minimum total cost.

输入格式

The first line contains n (1..100000), the second line contains n center coordinates, and the third line contains n destination coordinates, all in 1..10⁹.

输出格式

Output a single integer, the answer.

样例 1

输入：

3
1 2 2
5 2 4

输出：

6

样例 2

输入：

1
1
9

输出：

8

样例 3

输入：

2
4 1
1 4

输出：

0

样例说明

Example 1: after sorting, pair 1→2, 2→4 and 2→5, for a distance of 1+2+3=6. Example 2: the only distance is 8. Example 3: identical coordinates are paired with each other, costing 0.