#include <cstdio>
 
typedef long long LL;
const int MN = 100005;
 
int N, A[MN];
LL S;
 
int main() {
	scanf("%d", &N);
	for (int i = 1; i <= N; ++i) scanf("%d", &A[i]), S += A[i];
	if (S % ((LL)N * (N + 1) / 2) != 0) return puts("NO"), 0;
	LL C = S / ((LL)N * (N + 1) / 2);
	for (int i = 1; i <= N; ++i) {
		LL k = C - (A[i % N + 1] - A[i]);
		if (k < 0 || k % N != 0) return puts("NO"), 0;
	}
  
  
	puts("YES");
	return 0;
}
### Prompt

Your task is to create 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 <cstdio>
 
typedef long long LL;
const int MN = 100005;
 
int N, A[MN];
LL S;
 
int main() {
	scanf("%d", &N);
	for (int i = 1; i <= N; ++i) scanf("%d", &A[i]), S += A[i];
	if (S % ((LL)N * (N + 1) / 2) != 0) return puts("NO"), 0;
	LL C = S / ((LL)N * (N + 1) / 2);
	for (int i = 1; i <= N; ++i) {
		LL k = C - (A[i % N + 1] - A[i]);
		if (k < 0 || k % N != 0) return puts("NO"), 0;
	}
  
  
	puts("YES");
	return 0;
}
```