#include <bits/stdc++.h>
#define int long long
using namespace std;

signed main(){
  int N;
  cin>>N;
  std::vector<int> v(N);
  for(int i=0;i<N;i++)cin>>v[i];
  int sum=0;
  for(int i=0;i<N;i++)sum+=v[i];
  int out=0;
  out+=sum%(N*(N+1)/2);
  sum/=(N*(N+1)/2);
  std::vector<int> w(N,sum);
  for(int i=0;i<N;i++)w[i]-=v[(i+1)%N]-v[i];
  int a=0;
  for(int i=0;i<N;i++){
    if(w[i]<0)out++;
    out+=w[i]%N;
    a+=w[i]/N;
  }
  out+=abs(a-sum);
  if(out)cout<<"NO"<<endl;
  else cout<<"YES"<<endl;
}

### Prompt

In cpp, your task is to solve the following problem:

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

### Response

```cpp
#include <bits/stdc++.h>
#define int long long
using namespace std;

signed main(){
  int N;
  cin>>N;
  std::vector<int> v(N);
  for(int i=0;i<N;i++)cin>>v[i];
  int sum=0;
  for(int i=0;i<N;i++)sum+=v[i];
  int out=0;
  out+=sum%(N*(N+1)/2);
  sum/=(N*(N+1)/2);
  std::vector<int> w(N,sum);
  for(int i=0;i<N;i++)w[i]-=v[(i+1)%N]-v[i];
  int a=0;
  for(int i=0;i<N;i++){
    if(w[i]<0)out++;
    out+=w[i]%N;
    a+=w[i]/N;
  }
  out+=abs(a-sum);
  if(out)cout<<"NO"<<endl;
  else cout<<"YES"<<endl;
}

```