Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

5
4 5 1 2 3

Sample Output 1

YES

All the stones can be removed in one operation by selecting the second box.

Sample Input 2

5
6 9 12 10 8

Sample Output 2

YES

Sample Input 3

4
1 2 3 1

Sample Output 3

NO

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
class Program{
	static void Main(){
		int n=int.Parse(Console.ReadLine());
		long[] a=Array.ConvertAll(Console.ReadLine().Split(),long.Parse);
		string ans="YES";
		long o=a[n-1],t=n;
		long[] h=new long[n];
		for(int i=0;i<n-1;i++){
			t+=i+1;
			o+=a[i];
			h[i]=a[i+1]-a[i];
		}
		h[n-1]=a[0]-a[n-1];
		if(o%t!=0){ans="NO";}
		else{
			o/=t;
			t=0;
			for(int i=0;i<n;i++){
				if(h[i]>o){ans="NO";break;}
				h[i]=Math.Abs(h[i]-o);
				if(h[i]%n!=0){ans="NO";break;}
				t+=h[i]/n;
			}
			if(o!=t){ans="NO";}
		}
		Console.WriteLine(ans);
	}
}