#include <iostream>
#include <stdio.h>
#define N 100005
using namespace std;
#define ll long long
 
ll a[N],b[N];
int main(){
	ll n,Max=0,flag=1,ans=0;
	scanf("%lld",&n);
	ll num=n;
	num=(n+1)*num/2;
	for(int i=0;i<=n;i++){
		if(i<n) scanf("%lld",&a[i]);
		if(i){
			b[i%n]=a[i%n]-a[i-1];
			Max=max(Max,b[i%n]);
		}
	}
	for(int i=0;i<n;i++){
		b[i]=Max-b[i];
		if(b[i]%n) flag=0;
		b[i]/=n;
		ans+=b[i]*(n-i);
	}
	if(flag && (a[n-1]-ans)%num==0 && ans<=a[n-1]){
		cout<<"YES"<<endl;
	}else{
		cout<<"NO"<<endl;
	}
 
}
### Prompt

Please formulate 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 <iostream>
#include <stdio.h>
#define N 100005
using namespace std;
#define ll long long
 
ll a[N],b[N];
int main(){
	ll n,Max=0,flag=1,ans=0;
	scanf("%lld",&n);
	ll num=n;
	num=(n+1)*num/2;
	for(int i=0;i<=n;i++){
		if(i<n) scanf("%lld",&a[i]);
		if(i){
			b[i%n]=a[i%n]-a[i-1];
			Max=max(Max,b[i%n]);
		}
	}
	for(int i=0;i<n;i++){
		b[i]=Max-b[i];
		if(b[i]%n) flag=0;
		b[i]/=n;
		ans+=b[i]*(n-i);
	}
	if(flag && (a[n-1]-ans)%num==0 && ans<=a[n-1]){
		cout<<"YES"<<endl;
	}else{
		cout<<"NO"<<endl;
	}
 
}
```