#include<iostream>
#include<algorithm>
#include<string>
#include<vector>
using namespace std;
long long n, a[100000], b;
int main() {
	cin >> n; for (int i = 0; i < n; i++) { cin >> a[i]; b += a[i]; }
	if (b % (n*(n + 1) / 2) != 0) { cout << "NO" << endl; return 0; }
	long long c = (b / (n*(n + 1) / 2));
	for (int i = 0; i < n; i++) {
		long long s = a[(i + 1) % n] - a[i];
		s *= -1; s += c;
		if (s < 0 || (s%n) != 0) { cout << "NO" << endl; return 0; }
	}
	cout << "YES" << endl;
	return 0;
}
### Prompt

Please create a solution in cpp 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<iostream>
#include<algorithm>
#include<string>
#include<vector>
using namespace std;
long long n, a[100000], b;
int main() {
	cin >> n; for (int i = 0; i < n; i++) { cin >> a[i]; b += a[i]; }
	if (b % (n*(n + 1) / 2) != 0) { cout << "NO" << endl; return 0; }
	long long c = (b / (n*(n + 1) / 2));
	for (int i = 0; i < n; i++) {
		long long s = a[(i + 1) % n] - a[i];
		s *= -1; s += c;
		if (s < 0 || (s%n) != 0) { cout << "NO" << endl; return 0; }
	}
	cout << "YES" << endl;
	return 0;
}
```