#include<iostream>
using namespace std;
typedef long long ll;
#define fr(i,n) for(int i=0;i<n;i++)

int main(){
  ll n,a[100010],b[100010],s=0,k;
  cin>>n;
  fr(i,n){
    cin>>a[i];
    s+=a[i];
  }
  if(s%((n*(n+1))/2)>0){
    cout<<"NO"<<endl;
    return 0;
  }
  k=s/((n*(n+1))/2);
  fr(i,n) b[i]=a[i]-a[(i+1)%n]+k;
  bool f=0;
  fr(i,n) if(b[i]<0 || b[i]%n>0) f=1;
  cout<<(f?"NO":"YES")<<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<iostream>
using namespace std;
typedef long long ll;
#define fr(i,n) for(int i=0;i<n;i++)

int main(){
  ll n,a[100010],b[100010],s=0,k;
  cin>>n;
  fr(i,n){
    cin>>a[i];
    s+=a[i];
  }
  if(s%((n*(n+1))/2)>0){
    cout<<"NO"<<endl;
    return 0;
  }
  k=s/((n*(n+1))/2);
  fr(i,n) b[i]=a[i]-a[(i+1)%n]+k;
  bool f=0;
  fr(i,n) if(b[i]<0 || b[i]%n>0) f=1;
  cout<<(f?"NO":"YES")<<endl;
}
```