Walk Alone has two rows of matches, each of which contains matches. He defines the distance between them as , where and represent the height of the -th match in the first row and the second row, respectively. Walk Alone wants to beautify the matches by shortening the distance, and you are asked to find out the minimum distance after performing at most one swap within one row. Note that the height can be negative.

输入描述:

The first line contains one integer , denoting the number of matches in each row.

The second and the third line both contains  integers, representing the height of matches in the first row and the second row, respectively. All of these numbers satisfy .

输出描述:

Print one line containing a single integer, the minimum distance you can get.

3
1 2 3
3 2 1

0

4
4 3 9 9
7 3 7 3

5

备注:

In the second example, one of the best strategies is to swap  and , and the minimum distance is .