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 i64 = long long;

int main() {
    int n;
    std::cin >> n;
    std::vector<int> a(n), b(n);
    for (auto &e : a) std::cin >> e;
    for (auto &e : b) std::cin >> e;
    std::set<std::pair<int, int>> s;
    for (int i = 0; i < n; i++) s.emplace(-b[i], i);

    i64 ret = 0;
    while (!s.empty()) {
        auto c = s.begin();
        int i = c->second;
        int p = b[(i + 1) % n] + b[(i + n - 1) % n];
        if ((b[i] - a[i]) % p == 0) {
            ret += (b[i] - a[i]) / p;
            b[i] = a[i];
            s.erase(c);
        } else {
            int k = (b[i] - 1) / p;
            ret += k;
            b[i] -= k * p;
            if (k == 0 || b[i] < a[i]) {
                std::cout << -1 << std::endl;
                return 0;
            }
            s.erase(c);
            s.emplace(-b[i], i);
        }
    }

    std::cout << ret << std::endl;

    return 0;
}
