Minimum Operations to Make Arrays Equal

Given integer arrays source and target of equal length. One operation chooses a prefix or a suffix and adds 1 to every element in it. Find the minimum number of operations; output −1 if source cannot be turned into target.

This site uses a standard input/output protocol.

输入格式

The first line contains n; the second line contains source; the third line contains target. 1≤n≤100000, and every element's absolute value is ≤10^13.

输出格式

Output the minimum number of operations, or −1.

样例 1

输入：

3
1 2 2
2 2 3

输出：

2

样例 2

输入：

2
0 0
2 3

输出：

3

样例 3

输入：

3
0 0 0
1 2 1

输出：

2

样例 4

输入：

1
5
8

输出：

3