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

long long n, a[100005], sum, z;

int main() {
  ios_base::sync_with_stdio(0);

cin >> n; z = n * (n + 1) / 2;
  for(int i = 0; i < n; ++i) cin >> a[i], sum += a[i];
a[n] = a[0];
if(sum % z) return cout << "NO\n", 0;
for(int i = 0; i < n; ++i)
  if(-a[i + 1] + a[i] + sum / z < 0 || (-a[i + 1] + a[i] + sum / z) % n) return cout << "NO\n", 0;
cout << "YES\n";
  return 0;
}
### 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;

long long n, a[100005], sum, z;

int main() {
  ios_base::sync_with_stdio(0);

cin >> n; z = n * (n + 1) / 2;
  for(int i = 0; i < n; ++i) cin >> a[i], sum += a[i];
a[n] = a[0];
if(sum % z) return cout << "NO\n", 0;
for(int i = 0; i < n; ++i)
  if(-a[i + 1] + a[i] + sum / z < 0 || (-a[i + 1] + a[i] + sum / z) % n) return cout << "NO\n", 0;
cout << "YES\n";
  return 0;
}
```