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
import java.util.*;

public class Main{
	public static void main(String[] args){
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();
		long[]a=new long[n];
		Arrays.setAll(a,i->s.nextInt());
		long sum=Arrays.stream(a).sum();
		if(sum%(n*(n+1L)/2)!=0) {
			System.out.println("NO");
			return;
		}
		long k=sum*2/n/(n+1);
		{
			long t=a[0]-a[n-1];
			for(int i=n-1;i>0;--i)
				a[i]-=a[i-1];
			a[0]=t;
		}
		for(int i=0;i<n;++i)
			a[i]=k-a[i];
		System.out.println(
				Arrays.stream(a).allMatch(i->i>=0&&i%n==0)&&
				Arrays.stream(a).sum()/n==k?"YES":"NO");
	}
}