#include <bits/stdc++.h>

#define rep(i, n) for (int i = 0; i < n; i++)

using namespace std;

typedef long long ll;

int main() {
  ll N, s = 0;
  cin >> N;
  vector<ll> A(N + 1);
  rep(i, N) cin >> A[i], s += A[i];
  ll b = N * (N + 1) / 2;
  if (s % b != 0) return cout << "NO\n", 0;
  ll t = s / b;
  A[N] = A[0];
  rep(i, N) {
    ll d = A[i] + t - A[i + 1];
    if (d < 0 || d % N != 0) return cout << "NO\n", 0;
  }
  cout << "YES\n";
}

### Prompt

Please formulate 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>

#define rep(i, n) for (int i = 0; i < n; i++)

using namespace std;

typedef long long ll;

int main() {
  ll N, s = 0;
  cin >> N;
  vector<ll> A(N + 1);
  rep(i, N) cin >> A[i], s += A[i];
  ll b = N * (N + 1) / 2;
  if (s % b != 0) return cout << "NO\n", 0;
  ll t = s / b;
  A[N] = A[0];
  rep(i, N) {
    ll d = A[i] + t - A[i + 1];
    if (d < 0 || d % N != 0) return cout << "NO\n", 0;
  }
  cout << "YES\n";
}

```