#include<bits/stdc++.h>

using namespace std;

typedef long long int ll;

int main () {
  ios_base::sync_with_stdio(false);
  cin.tie(0);cout.tie(0);

  int n;
  cin >> n;
  vector < int > a (n);
  ll sum = 0, mx = ((ll)n * (n + 1)) / 2;
  for (auto &i : a) cin >> i, sum += i;

  if (sum % mx != 0) {
    cout << "NO\n";
    return 0;
  }

  ll k = sum / mx;

  for (int i = 1; i < n; i++) {
    int d = a[i] - a[i - 1];
    ll val = k - d;
    if (val < 0 || val % n != 0) {
      cout << "NO\n";
      return 0;
    }
  }

  cout << "YES\n";
}

### 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<bits/stdc++.h>

using namespace std;

typedef long long int ll;

int main () {
  ios_base::sync_with_stdio(false);
  cin.tie(0);cout.tie(0);

  int n;
  cin >> n;
  vector < int > a (n);
  ll sum = 0, mx = ((ll)n * (n + 1)) / 2;
  for (auto &i : a) cin >> i, sum += i;

  if (sum % mx != 0) {
    cout << "NO\n";
    return 0;
  }

  ll k = sum / mx;

  for (int i = 1; i < n; i++) {
    int d = a[i] - a[i - 1];
    ll val = k - d;
    if (val < 0 || val % n != 0) {
      cout << "NO\n";
      return 0;
    }
  }

  cout << "YES\n";
}

```