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 $A_{i + 1}$.

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.

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.