#include <cstdio>
const int MAXN = 1e5;
typedef long long LL;
int A[MAXN];
bool check(int N)
{
	int i, K, t;
	LL sum = 0;
	for(i=0; i<N; ++i)
		sum += A[i];
	if(sum % (LL(1+N)*N/2))
		return 0;
	K = sum / (LL(1+N)*N/2);
	for(i=0; i<N; ++i)
	{
		t = A[i]-A[(i-1+N)%N]-K;
		if(t%N || t>0)
			return 0;
	}
	return 1;
}
int main()
{
	int N, i;
	scanf("%d", &N);
	for(i=0; i<N; ++i)
		scanf("%d", A+i);
	puts(check(N) ? "YES" : "NO"); 
}
### Prompt

Your challenge is to write 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>
const int MAXN = 1e5;
typedef long long LL;
int A[MAXN];
bool check(int N)
{
	int i, K, t;
	LL sum = 0;
	for(i=0; i<N; ++i)
		sum += A[i];
	if(sum % (LL(1+N)*N/2))
		return 0;
	K = sum / (LL(1+N)*N/2);
	for(i=0; i<N; ++i)
	{
		t = A[i]-A[(i-1+N)%N]-K;
		if(t%N || t>0)
			return 0;
	}
	return 1;
}
int main()
{
	int N, i;
	scanf("%d", &N);
	for(i=0; i<N; ++i)
		scanf("%d", A+i);
	puts(check(N) ? "YES" : "NO"); 
}
```