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<iostream>
#include<algorithm>
#include<vector>
using namespace std;
typedef long long ll;
#define mod 1000000007
#define N 200010
ll a[N],b[N],n,ans;
void calc(){
    for(int i=0;i<n;i++){
	int j=(i+1)%n,k=(i+2)%n;
	ll p=b[i]+b[k];
	ll cnt=(b[j]-a[j])/p;
	ans+=cnt;
	b[j]-=cnt*p;
	//cout<<p<<" "<<cnt<<" "<<(b[j]-a[j])<<":";
    }
    //for(int i=0;i<n;i++)cout<<b[i]<<" ";cout<<endl;
}
int main(){
  cin>>n;
  for(int i=0;i<n;i++)cin>>a[i];
  for(int i=0;i<n;i++)cin>>b[i];
  ans=0;
  for(int i=0;i<100;i++)calc();
  bool ok=1;
  for(int i=0;i<n;i++)ok&=(a[i]==b[i]);
  if(ok)cout<<ans<<endl;
  else cout<<-1<<endl;
  return 0;
}
