#include <bits/stdc++.h>
using namespace std;
int main(){
	int N; 
	cin >> N; 
	long long int A[100010] = {}; 
	long long int S = 0; 
	for(int i = 0; i < N; i++){
		cin >> A[i]; 
		S += A[i]; 
	}
	A[N] = A[0]; 
	bool possible = true; 
  	long long int sum = (long long) N * (N + 1) / 2; 
	if(S % sum != 0) possible = false; 
	else{
		long long int T = S / sum; // 操作回数
		for(int i = 0; i < N; i++){
			long long int a = T - (A[i+1] - A[i]); 
			if(a < 0 || a % (long long) N != 0){
				possible = false; break;
			}
		}
	}
	if(possible) cout << "YES" << endl;
	else cout << "NO" << endl; 
}
### Prompt

Construct a cpp code solution to the problem outlined:

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;
int main(){
	int N; 
	cin >> N; 
	long long int A[100010] = {}; 
	long long int S = 0; 
	for(int i = 0; i < N; i++){
		cin >> A[i]; 
		S += A[i]; 
	}
	A[N] = A[0]; 
	bool possible = true; 
  	long long int sum = (long long) N * (N + 1) / 2; 
	if(S % sum != 0) possible = false; 
	else{
		long long int T = S / sum; // 操作回数
		for(int i = 0; i < N; i++){
			long long int a = T - (A[i+1] - A[i]); 
			if(a < 0 || a % (long long) N != 0){
				possible = false; break;
			}
		}
	}
	if(possible) cout << "YES" << endl;
	else cout << "NO" << endl; 
}
```