#include <iostream>
#include <algorithm>
using namespace std;
typedef long long int ll;
ll N;
ll a[100001];
ll d[100001];
ll sum;
ll k;
int main(){
  bool f=true;
  cin >> N;
  for(int i=0;i<N;i++){cin >> a[i];sum+=a[i];}
  ll t;
  t=(N*(N+1)/2);
  if(sum%t!=0){cout << "NO" << endl; return 0;}
  k=sum/t;
  for(int i=0;i<N;i++){
    d[i]=a[(i+1)%N]-a[i];
    d[i]-=k;
  }
  for(int i=0;i<N;i++){
    if(!(d[i]<=0 && abs(d[i])%N==0))f=false;
  }
  if(f==true)cout << "YES" << endl;
  else cout << "NO" << endl;
  return 0;
}

### Prompt

Generate 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>
#include <algorithm>
using namespace std;
typedef long long int ll;
ll N;
ll a[100001];
ll d[100001];
ll sum;
ll k;
int main(){
  bool f=true;
  cin >> N;
  for(int i=0;i<N;i++){cin >> a[i];sum+=a[i];}
  ll t;
  t=(N*(N+1)/2);
  if(sum%t!=0){cout << "NO" << endl; return 0;}
  k=sum/t;
  for(int i=0;i<N;i++){
    d[i]=a[(i+1)%N]-a[i];
    d[i]-=k;
  }
  for(int i=0;i<N;i++){
    if(!(d[i]<=0 && abs(d[i])%N==0))f=false;
  }
  if(f==true)cout << "YES" << endl;
  else cout << "NO" << endl;
  return 0;
}

```