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
#include<iostream>
using namespace std;
long long a[100010],T,n,tot,s,tt;
int main()
{
	cin>>n;s=n*(n+1)/2;
	for(int i=1;i<=n;i++) cin>>a[i],tot+=a[i];
	if(tot%s!=0) return puts("NO"),0;
	T=tot/s;a[n+1]=a[1];
	for(int i=1;i<=n;i++)
		if((T+a[i]-a[i+1])%n||T+a[i]-a[i+1]<0)
			return puts("NO"),0;
		else tt+=(T+a[i]-a[i+1])/n;
	tt==T?puts("YES"):puts("NO");
}
