#include<cstdio>
int n,a[100001];
long long S,T;
int main(){
	scanf("%d",&n);
	if(n==1) return 0*puts("YES");
	T=(long long)n*(n+1)/2;
	for(int i=1;i<=n;++i)
		scanf("%d",a+i), S+=a[i];
	if(S%T) return 0*puts("NO");
	S/=T;
	a[0]=a[n];
	for(int i=n;i>=1;--i)
		a[i]=a[i]-a[i-1];
	for(int i=1;i<=n;++i)
		a[i]-=S;
	int ok=1;
	for(int i=1;i<=n;++i)
		if(a[i]>0||a[i]%n) ok=0;
	puts(ok?"YES":"NO");
	return 0;
}
### Prompt

Create a solution in CPP for 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>
int n,a[100001];
long long S,T;
int main(){
	scanf("%d",&n);
	if(n==1) return 0*puts("YES");
	T=(long long)n*(n+1)/2;
	for(int i=1;i<=n;++i)
		scanf("%d",a+i), S+=a[i];
	if(S%T) return 0*puts("NO");
	S/=T;
	a[0]=a[n];
	for(int i=n;i>=1;--i)
		a[i]=a[i]-a[i-1];
	for(int i=1;i<=n;++i)
		a[i]-=S;
	int ok=1;
	for(int i=1;i<=n;++i)
		if(a[i]>0||a[i]%n) ok=0;
	puts(ok?"YES":"NO");
	return 0;
}
```