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<int,int> Pii;
typedef pair<ll,ll> Pll;
#define rep(i,n) for (ll i=0;i<n;++i)
const ll MOD=1000000007;

int main(){
    int N;
    cin >> N;
    vector<ll> A(N),B(N);
    rep (i,N){
        cin >> A[i];
    }
    rep (i,N){
        cin >> B[i];
    }
    ll ans=0;
    bool c=true;
    while(c){
        c=false;
        rep (i,N){
            int a=B[(i-1+N)%N]+B[(i+1)%N];
            if (B[i]-A[i]>=a){
                int b=(B[i]-A[i])/a;
                B[i]-=a*b;
                ans+=b;
                c=true;
            }
        }
    }
    if (A==B){
        cout << ans << endl;
    }
    else {
        cout << -1 << endl;
    }
}