There are N positive integers arranged in a circle.

Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:

* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.



Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.

Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.

Constraints

* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 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_N
B_1 B_2 ... B_N


Output

Print the minimum number of operations required, or `-1` if the objective cannot be achieved.

Examples

Input

3
1 1 1
13 5 7


Output

4


Input

4
1 2 3 4
2 3 4 5


Output

-1


Input

5
5 6 5 2 1
9817 1108 6890 4343 8704


Output

25
#include <bits/stdc++.h>

using namespace std;

const int kN = 2e5+7;

int n;
long long res;
int a[kN], b[kN];

int main()
{
    cin >> n;
    for (int i = 0; i < n; ++i)
        cin >> a[i];
    for (int i = 0; i < n; ++i) {
        cin >> b[i];
        if (b[i] < a[i]) {
            cout << "-1" << endl;
            return 0;
        }
    }
    int flag = 1;
    while (flag) {
        flag = 0;
        for (int i = 0; i < n; ++i) {
            int bt = b[(i-1+n)%n]+b[(i+1)%n];
            if (b[i]-bt >= a[i]) {
                int k = (b[i]-a[i])/bt;
                res += k;
                b[i] -= k*bt;
                flag = 1;
            }
        }
    }
    for (int i = 0; i < n; ++i) {
        if (a[i] != b[i]) {
            cout << "-1" << endl;
            return 0;
        }
    }
    cout << res << endl;
    return 0;
}