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
{
    class Program
    {
        static void Main(string[] args)
        {
            long n = long.Parse(Console.ReadLine());
            long[] x = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long times = x.Sum() / (n * (n + 1) / 2);
            long count = 0; long a = 0;
            bool flag = true;
            for (int i = 0; i < n; i++)
            {
                long dis = x[(i + 1) % n] - x[i];
                if ((times - dis) % n != 0) flag = false;
                count += (times - dis) / n;
                if (i + 1 < n) a += (n - 1 - i) * ((times - dis) / n);
                else a += n * ((times - dis) / n);
            }
            if (flag && count == times && x.Min() >= times && a == x[n - 1]) Console.WriteLine("YES");
            else Console.WriteLine("NO");
        }
    }
}