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 int ll;

int main () {
  ios_base::sync_with_stdio(false);
  cin.tie(0);cout.tie(0);

  int n;
  cin >> n;
  vector < int > a(n), b (n);
  for (auto &i : a) cin >> i;
  for (auto &i : b) cin >> i;
  ll moves = 0;
  priority_queue < pair < int, int > > q;
  for (int i = 0; i < n; i++) q.push ({b[i], i});

  while (!q.empty()) {
    int u = q.top().second;
    q.pop();
    int l = u - 1, r = u + 1;
    if (l < 0) l = n - 1;
    if (r == n) r = 0;

    int k = (b[u] - a[u]) / (b[l] + b[r]);
    if (b[u] != a[u] && k <= 0) {
      cout << -1 << '\n';
      return 0;
    }
    b[u] -= k * (b[l] + b[r]);
    moves += k;

    if (b[u] != a[u]) q.push ({b[u], u});
  }

  cout << moves << '\n';
}
