#include<bits/stdc++.h>
using namespace std;
int n;
long long int a[111111];
bool proc(){
	long long int s = 0;
	cin>>n;
	for(int i=0; i<n; i++){
		cin>>a[i];
		s += a[i];
	}
	long long int t = (1LL + n) * n / 2;
	if(s%t != 0)return false;
	s /= t;
	a[n] = a[0];
	long long int s2 = 0;
	for(int i=1; i<=n; i++){
		long long int w = -(a[i] - a[i-1] - s);
		if(w % n != 0 || w < 0)return false;
		s2 += w/n;
	}
	return s == s2;
}
int main(){
	cout << (proc()?"YES":"NO") <<endl;
	return 0;
}

### Prompt

Generate 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;
int n;
long long int a[111111];
bool proc(){
	long long int s = 0;
	cin>>n;
	for(int i=0; i<n; i++){
		cin>>a[i];
		s += a[i];
	}
	long long int t = (1LL + n) * n / 2;
	if(s%t != 0)return false;
	s /= t;
	a[n] = a[0];
	long long int s2 = 0;
	for(int i=1; i<=n; i++){
		long long int w = -(a[i] - a[i-1] - s);
		if(w % n != 0 || w < 0)return false;
		s2 += w/n;
	}
	return s == s2;
}
int main(){
	cout << (proc()?"YES":"NO") <<endl;
	return 0;
}

```