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.io.IOException;
import java.io.InputStream;
import java.util.NoSuchElementException;
import java.util.Collections;
import java.util.Arrays;
import java.lang.Math;
import java.util.PriorityQueue;
import java.util.Comparator;
import java.util.ArrayDeque;

public class Main {
	public static void main(String[] args) {
		FS reader = new FS();
		// write reader
		int N = reader.nextInt();
		int[] A = new int[N];
		int[] B = new int[N];
		for(int i=0; i<N; i++) {
		    A[i] = reader.nextInt();
		}
		for(int i=0; i<N; i++) {
		    B[i] = reader.nextInt();
		}
		solver(N, A, B);
	}
	
	public static void solver(int N, int[] A, int[] B) {
		// write logic
		ArrayDeque<Integer> q = new ArrayDeque<Integer>();
		for(int i=0; i<N; i++) {
		    q.add(i);
		}

		long ans = 0;
		while(!q.isEmpty()) {
		    int idx = q.poll();
		    if (B[idx] == A[idx]) continue;

	        int dif = B[(N+idx-1)%N]+B[(N+idx+1)%N];
	        int loop = (B[idx]-A[idx])/dif;
	        ans += loop;
	        B[idx] -= dif*loop;
	        if (loop > 0) {
	            q.add((N+idx-1)%N);
	            q.add((N+idx+1)%N);
	        }
		}
		boolean valid = true;
		for(int i=0; i<N; i++) {
		    if (A[i] != B[i]) valid = false;
		}
		if (valid) System.out.println(ans);
		else System.out.println(-1);
	}
	
	// Read Class
	static class FS {
		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() { return hasNextByte() ? buffer[ptr++] : -1;}
		private boolean isPrintableChar(int c) {return 33 <= c && c <= 126;}
		private void skipUnprintable() {while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
	
		public boolean hasNext() { skipUnprintable(); 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 int nextInt() {
			return (int)nextLong();
		}
		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();
			}
		}
	}
}
