#include <bits/stdc++.h>
using namespace std;
#define LL long long
int const SIZE=100009;

int main(){
	LL n;
	cin>>n;
	LL arr[SIZE];
	LL sum=0;
	for(int i=0;i<n;i++){
		cin>>arr[i];
		sum+=arr[i];
	}
	LL r=(2*sum)/(n*((n+1)));
	if((((2*sum)%(n*((n+1))))!=0)||(r<=0)){
		cout<<"NO";
		return 0;
	}
	for(int i=0;i<n;i++){
		int tn=(r-(arr[(i+1)%n]-arr[i%n]));
		if((tn%n!=0)||(tn<0)){
			cout<<"NO";
			return 0;
		}
	}
	cout<<"YES";
	return 0;
}
### Prompt

Please provide a cpp coded solution to the problem described below:

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;
#define LL long long
int const SIZE=100009;

int main(){
	LL n;
	cin>>n;
	LL arr[SIZE];
	LL sum=0;
	for(int i=0;i<n;i++){
		cin>>arr[i];
		sum+=arr[i];
	}
	LL r=(2*sum)/(n*((n+1)));
	if((((2*sum)%(n*((n+1))))!=0)||(r<=0)){
		cout<<"NO";
		return 0;
	}
	for(int i=0;i<n;i++){
		int tn=(r-(arr[(i+1)%n]-arr[i%n]));
		if((tn%n!=0)||(tn<0)){
			cout<<"NO";
			return 0;
		}
	}
	cout<<"YES";
	return 0;
}
```