#include<iostream>
#include<algorithm>
#define LL long long
LL N;
LL A[100010];
LL sum;

int main() {
	std::cin >> N;
	for (int i = 1; i <= N; i++) {
		std::cin >> A[i];
		sum += A[i];
		if (i == N)A[0] = A[N];
	}
	LL D = ((N + 1)*N) / 2;
	if (sum%D) {
		std::cout << "NO" << std::endl;
		return 0;
	}
	LL ave = sum / D;
	for (int i = 1; i < N; i++) {
		LL tmp = A[i] - A[i - 1];
		if (tmp > ave || (ave - tmp) % N) {
			std::cout << "NO" << std::endl;
			return 0;
		}
	}
	std::cout << "YES" << std::endl;
	return 0;
}
### 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<iostream>
#include<algorithm>
#define LL long long
LL N;
LL A[100010];
LL sum;

int main() {
	std::cin >> N;
	for (int i = 1; i <= N; i++) {
		std::cin >> A[i];
		sum += A[i];
		if (i == N)A[0] = A[N];
	}
	LL D = ((N + 1)*N) / 2;
	if (sum%D) {
		std::cout << "NO" << std::endl;
		return 0;
	}
	LL ave = sum / D;
	for (int i = 1; i < N; i++) {
		LL tmp = A[i] - A[i - 1];
		if (tmp > ave || (ave - tmp) % N) {
			std::cout << "NO" << std::endl;
			return 0;
		}
	}
	std::cout << "YES" << std::endl;
	return 0;
}
```