#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);

  ll n;cin>>n;
  ll sum=0;
  ll a[n];
  for(int i=0;i<n;i++){
      cin>>a[i];
      sum+=a[i];
  }
  ll tmp=n*(n+1)/2;
  if(sum%tmp!=0){
      cout<<"NO"<<endl;
      return 0;
  }
  sum/=tmp;
  ll k=0;
  bool ret=true;
  for(int i=0;i<n;i++){
      ll dif=-(a[(i+1)%n]-a[i]-sum);
      k+=dif/n;
      if(dif%n!=0||dif<0) ret=false;
  }
  if(ret&&(k==sum)) cout<<"YES"<<endl;
  else cout<<"NO"<<endl;
}

### Prompt

Your challenge is to write a Cpp solution to 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>

using namespace std;

typedef long long ll;

int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);

  ll n;cin>>n;
  ll sum=0;
  ll a[n];
  for(int i=0;i<n;i++){
      cin>>a[i];
      sum+=a[i];
  }
  ll tmp=n*(n+1)/2;
  if(sum%tmp!=0){
      cout<<"NO"<<endl;
      return 0;
  }
  sum/=tmp;
  ll k=0;
  bool ret=true;
  for(int i=0;i<n;i++){
      ll dif=-(a[(i+1)%n]-a[i]-sum);
      k+=dif/n;
      if(dif%n!=0||dif<0) ret=false;
  }
  if(ret&&(k==sum)) cout<<"YES"<<endl;
  else cout<<"NO"<<endl;
}

```