Score : $500$ points

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 $A_{i + 1}$.
• 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.

3
3 1 4
6 2 0

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.

3
1 1 1
1 1 2

-1

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

5
5 4 1 3 2
5 4 1 3 2

0

$A$ may equal $B$ before doing any operation.

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

7