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 "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<ll, int> P;
const int INF = (1<<30);
const ll INFLL = (1ll<<60);
const ll MOD = (ll)(1e9+7);

#define l_ength size

void mul_mod(ll& a, ll b){
	a *= b;
	a %= MOD;
}

void add_mod(ll& a, ll b){
	a = (a<MOD)?a:(a-MOD);
	b = (b<MOD)?b:(b-MOD);
	a += b;
	a = (a<MOD)?a:(a-MOD);
}

priority_queue<P> pq;

ll a[225816],b[225816];

int main(void){
	int n,i;
	ll x,y,z,ans=0ll,tmp;
	P p;
	cin >> n;
	for(i=0; i<n; ++i){
		cin >> a[i];
	}
	for(i=0; i<n; ++i){
		cin >> b[i];
		pq.push(P(b[i],i));
	}
	while(!pq.empty()){
		p = pq.top();
		pq.pop();
		i = p.second;
		x = b[(i+n-1)%n];
		z = b[(i+1)%n];
		tmp = (b[i]-a[i])/(x+z);
		ans += tmp;
		b[i] -= (x+z)*tmp;
		if(tmp && b[i]>a[i]){
			pq.push(P(b[i],i));
		}
	}
	for(i=0; i<n; ++i){
		if(a[i]-b[i]){
			cout << -1 << endl;
			return 0;
		}
	}
	cout << ans << endl;
	return 0;
}
