#include<bits/stdc++.h>
using namespace std;
long long n,x[100010],tot,md,tmp,idx,cnt,tmpcnt,temp,diff;
bool ok;
int main()
{
	scanf("%lld",&n);
	for(int i=0;i<n;i++)
	{
		scanf("%lld",&x[i]);
		tot+=x[i];
	}
	md = (n*(n+1))/2;
	if(tot%md) printf("NO\n");
	else
	{	
		ok = 1;
		cnt = 1;
		tmp = tot/md;
		for(long long i=0;i<n;i++)
		{
			diff = x[(i+1)%n]-x[i]-tmp;
			if(diff>0 ||abs(diff)%n) 
			{
				ok = 0;
				break;
			}
		}
		printf("%s\n",ok?"YES":"NO");	
	}
	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<bits/stdc++.h>
using namespace std;
long long n,x[100010],tot,md,tmp,idx,cnt,tmpcnt,temp,diff;
bool ok;
int main()
{
	scanf("%lld",&n);
	for(int i=0;i<n;i++)
	{
		scanf("%lld",&x[i]);
		tot+=x[i];
	}
	md = (n*(n+1))/2;
	if(tot%md) printf("NO\n");
	else
	{	
		ok = 1;
		cnt = 1;
		tmp = tot/md;
		for(long long i=0;i<n;i++)
		{
			diff = x[(i+1)%n]-x[i]-tmp;
			if(diff>0 ||abs(diff)%n) 
			{
				ok = 0;
				break;
			}
		}
		printf("%s\n",ok?"YES":"NO");	
	}
	return 0;
}
```