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;
using System.Linq;

namespace AGC010_B___Boxes
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine(solver() ? "YES" : "NO");
        }
        static bool solver()
        {
            var N = long.Parse(Console.ReadLine());
            var A = Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);

            var difference = new long[N];
            difference[0] = A[0] - A[N - 1];
            for (int i = 1; i < N; i++) difference[i] = A[i] - A[i - 1];

            if ((A.Sum() % (N * (N + 1) / 2) != 0))return false;
            var opCount = A.Sum() / (N * (N + 1) / 2);
            for (int i = 0; i < N; i++)
            {
                var check = (difference[i] - opCount) * -1;
                if (check < 0 || check % N != 0) return false;
            }
            return true;
        }
    }
}