Problem Statement

Given are two sequences of length N each: $A = (A_1, A_2, A_3, \dots, A_N)$ and $B = (B_1, B_2, B_3, \dots, B_N)$.
Determine whether it is possible to make A equal B by repeatedly doing the operation below (possibly zero times). If it is possible, find the minimum number of operations required to do so.

• Choose an integer i such that $1 \le i \lt N$, and do the following in order:
• swap A_i and A_{i + 1};
• add 1 to A_i;
• subtract 1 from A_{i + 1}.

Input

Input is given from Standard Input in the following format:
N
$A_1 A_2 A_3 \dots A_N$
$B_1 B_2 B_3 \dots B_N$

Output

If it is impossible to make A equal B, print -1.
Otherwise, print the minimum number of operations required to do so.

Constraints

• $2 \le N \le 2 \times 10^5$
• $0 \le A_i \le 10^9$
• $0 \le B_i \le 10^9$
• All values in input are integers.

Sample Input 1

3
3 1 4
6 2 0

Sample Output 1

2

We can match A with B in two operations, as follows:

• First, do the operation with i = 2, making A = (3, 5, 0).
• Next, do the operation with i = 1, making A = (6, 2, 0).

We cannot meet our objective in one or fewer operations.

Sample Input 2

3
1 1 1
1 1 2

Sample Output 2

-1

In this case, it is impossible to match A with B.

Sample Input 3

5
5 4 1 3 2
5 4 1 3 2

Sample Output 3

0

A may equal B before doing any operation.

Sample Input 4

6
8 5 4 7 4 5
10 5 6 7 4 1

Sample Output 4

7

见题面 Input 部分

见题面 Output 部分