#include<iostream>
using namespace std;
long n,a[1<<17],b[1<<17],sum;
int main()
{
	cin>>n;
	for(int i=0;i<n;i++)
	{
		cin>>a[i];
		sum+=a[i];
		if(i)
		{
			b[i-1]=a[i]-a[i-1];
		}
	}
	b[n-1]=a[0]-a[n-1];
	long all=-~n*n/2;
	if(sum%all)
	{
		cout<<"NO"<<endl;
		return 0;
	}
	long k=sum/all;
	for(int i=0;i<n;i++)
	{
		b[i]-=k;
		if(b[i]>0||b[i]%n)
		{
			cout<<"NO"<<endl;
			return 0;
		}
	}
	cout<<"YES"<<endl;
}
### Prompt

Please create a solution in Cpp 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>
using namespace std;
long n,a[1<<17],b[1<<17],sum;
int main()
{
	cin>>n;
	for(int i=0;i<n;i++)
	{
		cin>>a[i];
		sum+=a[i];
		if(i)
		{
			b[i-1]=a[i]-a[i-1];
		}
	}
	b[n-1]=a[0]-a[n-1];
	long all=-~n*n/2;
	if(sum%all)
	{
		cout<<"NO"<<endl;
		return 0;
	}
	long k=sum/all;
	for(int i=0;i<n;i++)
	{
		b[i]-=k;
		if(b[i]>0||b[i]%n)
		{
			cout<<"NO"<<endl;
			return 0;
		}
	}
	cout<<"YES"<<endl;
}
```