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: Runtime Error)

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
class Program
{
	static void Main()
	{
		long n = long.Parse(Console.ReadLine());//int.Parseは文字列を整数に変換。
		long[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);
    long sumNums = 0;
    long sumCount = 0;
    long divideCount = 0;
    long[] diffrences = new long[n];
    long divideCheck = 0;

    for(long i = 0; i < n; i++)
    {
      sumCount += i+1;
      sumNums += nums[i];
      if(i != n-1) diffrences[i] = nums[i+1] - nums[i];
    }
    diffrences[n-1] = nums[0] - nums[n-1];
    
    if(sumNums % sumCount != 0) Console.WriteLine("NO");
    else
    {
      divideCount = sumNums / sumCount;
      for(long i = 0; i < n; i++)
      {
        diffrences[i] -= divideCount;
        diffrences[i] *= -1;
        divideCheck += diffrences[i]/(n-1);
      }
    }
    
    if(divideCheck == divideCount) Console.WriteLine("YES");
    else Console.WriteLine("NO");
	}
}