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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace B
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = long.Parse(Console.ReadLine());
            var temp = Console.ReadLine().Split(' ').ToList();
            var list = temp.Select(ln => long.Parse(ln)).ToList();
            
            long unit_sum = n * (n + 1) / 2;
            if (list.Sum() % unit_sum != 0) { Console.WriteLine("NO"); }
            int n_addition = (int)(list.Sum() / unit_sum);

            var diff = new List<int>();
            for (int i = 0; i < list.Count - 1; i++)
            {
                diff.Add((int)(list[i + 1] - list[i]));
            }
            diff.Add((int)(list[0] - list[list.Count - 1]));

            var diff2 = diff.Select(ln => ln - n_addition);

            if (diff2.All(ln => ln % n == 0) && diff2.Sum() == -n * n_addition) { Console.WriteLine("YES"); }
            else { Console.WriteLine("NO"); }
        }
    }
}