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;
using System.Collections.Generic;
class P
{
    static void Main()
    {
        long n = long.Parse(Console.ReadLine());
        long[] a = Console.ReadLine().Split().Select(long.Parse).ToArray();
        long asum = a.Sum();
        long sum = (n * (n + 1)) / 2;
        long diffsum = 0;
        if (asum % sum != 0)
        {
            Console.WriteLine("NO");
            return;
        }
        long opeCount = asum / sum;
        for (int i = 0; i < a.Length; i++)
        {
            long diff = a[(i + 1) % a.Length] - a[i];
            if ((opeCount - diff) % a.Length != 0)
            {
                Console.WriteLine("NO");
                return;
            }
            diffsum += diff;
        }
        if(diffsum / a.Length != opeCount)
        {
            Console.WriteLine("NO");
            return;
        }
        Console.WriteLine("YES");
    }
}