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.*;

class Main{
    public static void main(String[] args){
        FastScanner fsc=new FastScanner();
        int n=fsc.nextInt();
        long[] a=new long[n];
        long[] b=new long[n];
        PriorityQueue<Integer> pq=new PriorityQueue<>((u, v)->{
            if(b[u]==a[u]){
                if(b[v]==a[v]){
                    return Long.compare(b[v], b[u]);
                } else{
                    return 1;
                }
            } else{
                if(b[v]==a[v]){
                    return -1;
                } else{
                    return Long.compare(b[v], b[u]);
                }
            }
        });
        for(int i=0;i<n;i++){
            a[i]=fsc.nextLong();
        }
        for(int i=0;i<n;i++){
            b[i]=fsc.nextLong();
            if(b[i]>a[i]){
                pq.add(i);
            } else if(b[i]<a[i]){
                System.out.println(-1);
                return;
            }
        }
        fsc.close();
        long ans=0;
        while(!pq.isEmpty()){
            int i=pq.poll();
            if(a[i]==b[i]){
                break;
            }
            if(b[i]-(b[(n+i-1)%n]+b[(i+1)%n])<a[i]){
                System.out.println(-1);
                return;
            }
            long minus=b[(n+i-1)%n]+b[(i+1)%n];
            long max=Math.max(Math.max(b[(n+i-1)%n], b[(i+1)%n]), a[i]);
            long k=(b[i]-max)/minus;
            if(k>1){
                b[i]-=k*minus;
                ans+=k;
            } else{
                b[i]-=minus;
                ans++;
            }
            if(b[i]>a[i]){
                pq.add(i);
            }
        }
        System.out.println(ans);
    }

    static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        private boolean hasNextByte(){
            if(ptr<buflen) return true;
            else{
                ptr = 0;
                try{
                    buflen = in.read(buffer);
                }
                catch(IOException e){
                    e.printStackTrace();
                }
                if(buflen<=0) return false;
            }
        return true;
        }
        private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
        private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
        public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public long nextLong() {
            if (!hasNext()) throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) throw new NumberFormatException();
            while(true){
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                }
                else if(b == -1 || !isPrintableChar(b)) return minus ? -n : n;
                else throw new NumberFormatException();
                b = readByte();
            }
        }
        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
            return (int) nl;
        }
        public double nextDouble() { return Double.parseDouble(next());}
        public void close(){
            try{in.close();}
            catch(IOException e){e.printStackTrace();}
        }
    }
}
