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
import java.util.*;
import java.io.*;
import java.lang.*;
import java.math.*;
public class Main {
    public static void main(String[] args) throws Exception {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        int n = Integer.parseInt(bf.readLine());
        StringTokenizer st = new StringTokenizer(bf.readLine());
        long[] b = new long[n]; for(int i=0; i<n; i++) b[i] = Integer.parseInt(st.nextToken());
        st = new StringTokenizer(bf.readLine());
        long[] a = new long[n]; for(int i=0; i<n; i++) a[i] = Integer.parseInt(st.nextToken());
        boolean continueloop = true;
        long ans = 0;
        boolean[] diff = new boolean[n];
        for(int i=0; i<n; i++) diff[i] = (a[i]!=b[i]);
        while(continueloop) {
          continueloop = false;
          for(int i=1; i<=n; i++) {
            if(diff[i%n] && (a[i%n] >= 0L + a[i-1] + a[(i+1)%n])) {
              if((0L + a[i%n] - b[i%n]) % (0L + a[i-1] + a[(i+1)%n]) == 0) {
                ans += (int)((a[i%n] - b[i%n])/(0L + a[i-1] + a[(i+1)%n]));
                a[i%n] = b[i%n];
                diff[i%n] = false;
                continueloop = true;
                continue;
              }
              ans += (1L*a[i%n]/(0L +a[i-1] + a[(i+1)%n]));
              a[i%n] %= 0L + a[i-1] + a[(i+1)%n];
              diff[i%n] = (a[i%n]!=b[i%n]);
              if(a[i%n] < b[i%n]) {
                out.println("-1");
                out.close();
                System.exit(0);
              }
              continueloop = true;

              //continueloop = true;
            }
          }
        }
        for(int i=0; i<n; i++) {
          if(a[i] != b[i]) {
            out.println("-1");
            out.close();
            System.exit(0);
          }
        }
        out.println(ans);
        // int n = Integer.parseInt(st.nextToken());

        out.close(); System.exit(0);
    }
}
