There are N boxes arranged in a circle. The i-th box contains A_i stones.

Determine whether it is possible to remove all the stones from the boxes by repeatedly performing the following operation:

* Select one box. Let the box be the i-th box. Then, for each j from 1 through N, remove exactly j stones from the (i+j)-th box. Here, the (N+k)-th box is identified with the k-th box.



Note that the operation cannot be performed if there is a box that does not contain enough number of stones to be removed.

Constraints

* 1 ≦ N ≦ 10^5
* 1 ≦ A_i ≦ 10^9

Input

The input is given from Standard Input in the following format:


N
A_1 A_2 … A_N


Output

If it is possible to remove all the stones from the boxes, print `YES`. Otherwise, print `NO`.

Examples

Input

5
4 5 1 2 3


Output

YES


Input

5
6 9 12 10 8


Output

YES


Input

4
1 2 3 1


Output

NO
#include <bits/stdc++.h>
using namespace std;

int main()
{
    int n; cin>>n;
    vector<long> a(n);
    long s=0;
    for(auto& e: a) { cin>>e; s+=e; }

    auto m=n*(n+1L)/2;
    if (s%m>0) return cout<<"NO"<<endl, 0;

    int k=s/m;
    int t=0;
    for(int i=0; i<n; ++i) {
        auto e=a[(i+1)%n]-a[i]-k;
        if (e%n!=0 or e>0) return cout<<"NO"<<endl, 0;
        t+=-e/n;
    }
    cout<<(t==k ? "YES" : "NO")<<endl;
}
