#include<bits/stdc++.h>

using namespace std;

typedef long long LL;
#define N 120000

LL n,a[N],sum,m,p,num;

int main(){
	scanf("%lld",&n);
	for (LL i=1;i<=n;++i){
		scanf("%lld",a+i);
		sum+=a[i];
	}
	m=n*(n+1)/2;
	if (sum%m!=0){puts("NO"); return 0;}
	num=sum/m;
	a[0]=a[n];
	for (LL i=1;i<=n;++i){
		LL x=a[i]-a[i-1];
		if (num-x<0||(num-x)%n!=0){puts("NO"); return 0;}
		LL t=(num-x)/n;
		p+=t;
	}
	puts(p==num?"YES":"NO");
	
	return 0;
}
			
### Prompt

Your challenge is to write 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;

typedef long long LL;
#define N 120000

LL n,a[N],sum,m,p,num;

int main(){
	scanf("%lld",&n);
	for (LL i=1;i<=n;++i){
		scanf("%lld",a+i);
		sum+=a[i];
	}
	m=n*(n+1)/2;
	if (sum%m!=0){puts("NO"); return 0;}
	num=sum/m;
	a[0]=a[n];
	for (LL i=1;i<=n;++i){
		LL x=a[i]-a[i-1];
		if (num-x<0||(num-x)%n!=0){puts("NO"); return 0;}
		LL t=(num-x)/n;
		p+=t;
	}
	puts(p==num?"YES":"NO");
	
	return 0;
}
			
```