Strange Operation

Task

Doctor Strange found two integer arrays of length $N$, namely $A_0, \dots, A_{N-1}$ and $B_0, \dots, B_{N-1}$.
He can perform the following operation on $A$ any number of times:

• Choose an index $1 \leq i \leq N - 2$ and let $A_i := -(A_{i - 1} + A_i + A_{i + 1})$. That is, assign the value $-(A_{i - 1} + A_i + A_{i + 1})$ to $A_i$.

Help the Doctor determine whether it is possible to make the array $A$ equal to $B$ and if so, then find the minimum number of operations required to achieve this.

Input data

The first line contains the only integer $N$.
The second line contains $N$ integers, the elements of array $A$.
The third line contains $N$ integers, the elements of array $B$.

Output data

You need to write a single line with an integer: the minimum number of operations required to make $A$ equal to $B$, or $-1$ if it is not possible to do so.

Constraints and clarifications

• $2 \le N \le 2 \cdot 10^5$.
• $-10^9 \le A_i, B_i \le 10^9$ for each $i=0\ldots N-1$.

Scoring

In this task, you can get partial scores: you will get $50\%$ of the points for a subtask if you successfully determine whether it is possible to make $A$ equal to $B$ (but do not correctly solve all of its test cases).
For this, the following condition must be satisfied for all test cases in a subtask: you should output $-1$ whenever it is impossible to make the two arrays equal, and otherwise, you should output a non-negative integer between $0$ and $2^{63}-1$.

Example 1

stdin

6
2 7 1 8 2 8
2 -10 1 -11 1 8

stdout

3

Explanation

In the first sample case, consider the following steps for the array $A = [2,7,1,8,2,8]$:

• Perform the operation on index $3$. The array becomes: $[2,7,1,-11,2,8]$.
• Perform the operation on index $1$. The array becomes: $[2,-10,1,-11,2,8]$.
• Perform the operation on index $4$. The array becomes: $[2,-10,1,-11,1,8]$.

It is not possible to make the two arrays equal in less than $3$ moves.

Example 2

stdin

4
3 1 4 1
-4 1 -6 1

stdout

-1

Explanation

In the second sample case, it can be proven that there is no way to make $A$ equal to $B$ using the described operation.