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;

namespace AGC010B
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            long[] A = Console.ReadLine().Split(' ').Select(a => long.Parse(a)).ToArray();

            long onetime = N * (N + 1) / 2;

            long Sum = A.Sum();

            if (Sum % onetime != 0)
            {
                Console.WriteLine("No");
                return;
            }

            long times = Sum / onetime;
            
            long[] Difference = new long[N];
            for (int i = 0; i < N - 1; i++)
            {
                Difference[i] = Math.Abs(A[i + 1] - A[i] - times);
            }

            Difference[N - 1] = Math.Abs(A[0] - A[N - 1] - times);

            long count = 0;
            for (int i = 0; i < N; i++)
            {
                if (Difference[i] % N != 0)
                {
                    Console.WriteLine("No");
                    return;
                }

                count += Difference[i] / N;
            }

            if (count == times)
            {
                Console.WriteLine("Yes");
                return;
            }
            Console.WriteLine("No");
        }
    }
}