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: Wrong Answer)

using System;
using System.Linq;

public class Program
{
	public static void Main()
	{
		int N = int.Parse(Console.ReadLine());
		int[] A = Console.ReadLine().Split().Select(int.Parse).ToArray();
		for (int i = 0; i < N; i++)
		{
			var flag = true;
			for (int j = 1; j <= N; j++)
			{
				if (A[(i + j) % N] % j > 0)
				{
					flag = false;
					break;
				}
			}
			if (flag)
			{
				Console.WriteLine("YES");
				return;
			}
		}
		Console.WriteLine("NO");
	}
}