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.math.*;
public class Main{
	//Don't have to see. start------------------------------------------
	static class InputIterator{
		ArrayList<String> inputLine = new ArrayList<String>(1024);
		int index = 0; int max; String read;
		InputIterator(){
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			try{
				while((read = br.readLine()) != null){
					inputLine.add(read);
				}
			}catch(IOException e){}
			max = inputLine.size();
		}
		boolean hasNext(){return (index < max);}
		String next(){
			if(hasNext()){
				return inputLine.get(index++);
			}else{
				throw new IndexOutOfBoundsException("There is no more input");
			}
		}
	}
	static InputIterator ii = new InputIterator();//This class cannot be used in reactive problem.
	static PrintWriter out = new PrintWriter(System.out);
	static void flush(){out.flush();}
	static void myout(Object t){out.println(t);}
	static void myerr(Object t){System.err.print("debug:");System.err.println(t);}
	static String next(){return ii.next();}
	static boolean hasNext(){return ii.hasNext();}
	static int nextInt(){return Integer.parseInt(next());}
	static long nextLong(){return Long.parseLong(next());}
	static ArrayList<String> nextStrArray(){return myconv(next(), 8);}
	static ArrayList<String> nextCharArray(){return myconv(next(), 0);}
	static ArrayList<Integer> nextIntArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Integer> ret = new ArrayList<Integer>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Integer.parseInt(input.get(i)));
		}
		return ret;
	}
	static ArrayList<Long> nextLongArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Long> ret = new ArrayList<Long>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Long.parseLong(input.get(i)));
		}
		return ret;
	}
	static HashMap<Integer, String> CONVSTR = new HashMap<Integer, String>();
	static String myconv(Object list, int no){//only join
		String joinString = CONVSTR.get(no);
		if(list instanceof String[]){
			return String.join(joinString, (String[])list);
		}else if(list instanceof ArrayList){
			return String.join(joinString, (ArrayList)list);
		}else{
			throw new ClassCastException("Don't join");
		}
	}
	static ArrayList<String> myconv(String str, int no){//only split
		String splitString = CONVSTR.get(no);
		return new ArrayList<String>(Arrays.asList(str.split(splitString)));
	}
	public static void main(String[] args){
		CONVSTR.put(8, " "); CONVSTR.put(9, "\n"); CONVSTR.put(0, "");
		Runtime rt = Runtime.getRuntime();
		long mae = System.currentTimeMillis();
		solve();flush();
		long ato = System.currentTimeMillis();
		myerr("time : " + (ato - mae) + "ms");
		myerr("memory : " + ((rt.totalMemory() - rt.freeMemory()) / 1024) + "KB");
	}
	//Don't have to see. end------------------------------------------
	static void solve(){//Here is the main function
		int N = nextInt();
		ArrayList<Integer> alist = nextIntArray();
		ArrayList<Integer> blist = nextIntArray();
		QueueObject[] clList = new QueueObject[N];
		PriorityQueue<QueueObject> pq = new PriorityQueue<QueueObject>();
		for(int i = 0; i < N; i++){
			QueueObject q = new QueueObject(i, alist.get(i), blist.get(i));
			pq.add(q);
			clList[i] = q;
		}
		long output = 0;
		while(!pq.isEmpty()){
			QueueObject now = pq.poll();
			int mae = (now.no - 1 + N) % N;
			int ato = (now.no + 1) % N;
			int side = clList[mae].bv + clList[ato].bv;
			if(now.av % side == now.bv % side){
				output += (now.bv - now.av) / side;
				now.bv = now.av;
			}else{
				int ng = now.bv / side + 1;
				int ok = 0;
				while(Math.abs(ng - ok) > 1){
					int c = (ng + ok) / 2;
					if(now.av <= now.bv - side * c){
						ok = c;
					}else{
						ng = c;
					}
				}
				if(ok == 0){
					myout(-1);
					return;
				}
				output += ok;
				now.bv = now.bv - side * ok;
				pq.add(now);
			}
		}
		myout(output);
	}
	//Method addition frame start
  static class QueueObject implements Comparable<QueueObject>{
    int no;
    int av;
    int bv;
    QueueObject(int i, int a, int b){
      no = i;
      av = a;
      bv = b;
    }
    public int compareTo(QueueObject q){
      return q.bv - this.bv;
    }
  }

	//Method addition frame end
}
