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(){
  long long int n,k[100005],sum=0;
  cin>>n;
  for(int i=0;i<n;++i){
    cin>>k[i];
    sum+=k[i];
  }
  if(sum%(((1+n)*n)/2)){
    cout<<"NO"<<endl;
    return 0;
  }
  int mon=sum/(((1+n)*n)/2);
  long long int mo[100005];
  for(int i=0;i<n;++i){
    if(i!=n-1) mo[i]=k[i+1]-k[i]-mon;
    else mo[i]=k[0]-k[i]-mon;
    
    if(mo[i]>0||mo[i]%n){
      cout<<"NO"<<endl;
      return 0;
    }
  }
  
  cout<<"YES"<<endl;
}