#include <iostream>
#include <vector>
using namespace std;

int main() {
  long long N, S=0; cin >> N;
  vector<int> A(N),B(N);
  for(int i=0;i<N;++i) {
    cin >> A[i]; S+=A[i];
  }
  if(S%(N*(N+1)/2)) {
    cout << "NO" << endl; return 0;
  }
  int a=S/(N*(N+1)/2);
  for(int i=0;i<N;++i) B[i] = A[(i+1)%N]-A[i];
  for(int i=0;i<N;++i) {
    if((B[i]-a)%N||B[i]>a) {
      cout << "NO" << endl; return 0;
    }
  }
  cout << "YES" << endl;
  return 0;
}
### Prompt

Create a solution in Cpp for 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 <vector>
using namespace std;

int main() {
  long long N, S=0; cin >> N;
  vector<int> A(N),B(N);
  for(int i=0;i<N;++i) {
    cin >> A[i]; S+=A[i];
  }
  if(S%(N*(N+1)/2)) {
    cout << "NO" << endl; return 0;
  }
  int a=S/(N*(N+1)/2);
  for(int i=0;i<N;++i) B[i] = A[(i+1)%N]-A[i];
  for(int i=0;i<N;++i) {
    if((B[i]-a)%N||B[i]>a) {
      cout << "NO" << endl; return 0;
    }
  }
  cout << "YES" << endl;
  return 0;
}
```