#include <bits/stdc++.h>
using namespace std;

int main() {
  long long n;
  cin >> n;

  vector<long long> a(n);
  for (auto &i : a) cin >> i;

  long long cnt = 0, m = n * (n + 1) / 2;
  for (auto i : a) cnt += i;

  bool ans = true;
  if (cnt % m) ans = false;

  long long o = cnt / m;
  vector<long long> d;
  for (int i = 0; i < n; ++i) {
    d.push_back(a[i] - a[(i + 1) % n] + o);
  }

  cnt = 0;
  for (int i = 0; i < n; ++i) {
    if (d[i] % n || d[i] < 0) ans = false;
    cnt += d[i] / n;
  }

  if (cnt != o) ans = false;

  puts(ans ? "YES" : "NO");
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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;

int main() {
  long long n;
  cin >> n;

  vector<long long> a(n);
  for (auto &i : a) cin >> i;

  long long cnt = 0, m = n * (n + 1) / 2;
  for (auto i : a) cnt += i;

  bool ans = true;
  if (cnt % m) ans = false;

  long long o = cnt / m;
  vector<long long> d;
  for (int i = 0; i < n; ++i) {
    d.push_back(a[i] - a[(i + 1) % n] + o);
  }

  cnt = 0;
  for (int i = 0; i < n; ++i) {
    if (d[i] % n || d[i] < 0) ans = false;
    cnt += d[i] / n;
  }

  if (cnt != o) ans = false;

  puts(ans ? "YES" : "NO");
}

```