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;
typedef long long ll;

#define index(i) (((i) + n) % n)

int main(void)
{
    int n;
    cin >> n;
    vector<int> a(n);
    vector<int> b(n);
    ll count = 0;
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }
    for (int i = 0; i < n; i++) {
        cin >> b[i];
    }

    for (;;) {
        ll count1 = count;
        for (int i = 0; i < n; i++) {
            if (b[index(i-1)] + b[index(i+1)] <= b[index(i)]) {
                int s = b[index(i-1)] + b[index(i+1)];
                int t = (b[i] - a[i]) / s;
                b[index(i)] -= s*t;
                count += t;
            }
        }
        if (count1 == count) break;
    }
    for (int i = 0; i < n; i++) {
        if (a[i] != b[i]) {
            count = -1;
            break;
        }
    }
    cout << count << endl;
}

