#include<bits/stdc++.h>
using namespace std;

void fail(){
	cout<<"NO"<<endl;
	exit(0);
}
int a[100001];
int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n;
	cin>>n;
	for(int i=0;i<n;i++)
		cin>>a[i];
	a[n]=a[0];
	long long int tot=0;
	for(int i=0;i<n;i++)
		tot+=a[i];
	long long int sum=1LL*n*(n+1)/2;
	if(tot%sum!=0){
		cout<<"NO"<<endl;
		return 0;
	}
	long long int k=tot/sum;
	for(int i=0;i<n;i++){
		long long int x=k-a[i+1]+a[i];
		if(x<0||x%n!=0)
			fail();
	}
	cout<<"YES"<<endl;
}

### 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;

void fail(){
	cout<<"NO"<<endl;
	exit(0);
}
int a[100001];
int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n;
	cin>>n;
	for(int i=0;i<n;i++)
		cin>>a[i];
	a[n]=a[0];
	long long int tot=0;
	for(int i=0;i<n;i++)
		tot+=a[i];
	long long int sum=1LL*n*(n+1)/2;
	if(tot%sum!=0){
		cout<<"NO"<<endl;
		return 0;
	}
	long long int k=tot/sum;
	for(int i=0;i<n;i++){
		long long int x=k-a[i+1]+a[i];
		if(x<0||x%n!=0)
			fail();
	}
	cout<<"YES"<<endl;
}

```