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;

namespace agc010_b
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
            bool[] flag = new bool[n];
            for (int i = 0; i < n; i++)
            {
                flag[x[i] % n] = true;
            }
            bool ret = true;
            for (int i = 0; i < n; i++)
            {
                if (!flag[i])
                {
                    ret = false;
                }
            }
            Array.Sort(flag);
            Array.Reverse(flag);
            Array.Sort(x);
            int a = 0;
            for (int i = 1; i <= n; i++)
            {
                a += i;
            }
            long sum = x.Sum();
            Console.WriteLine(sum % a == 0 && sum / a <= x[0] && (ret || flag[0] != flag[1]) ? "YES" : "NO");
        }
    }
}