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 AtCoderCs
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            var a = new long[n];
            var values = Console.ReadLine().Split(' ');

            long temp = long.MaxValue;
            long most_small_index = -1;

            for (var i = 0; i < n; i++)
            {
                a[i] = long.Parse(values[i]);
                if (a[i] < temp)
                {
                    temp = a[i];
                    most_small_index = i;
                }
            }

            while (true)
            {
                var next_small = long.MaxValue;
                var next_small_index = -1;
                bool is_finished = true;

                for (int i = 0; i < n; i++)
                {
                    if (i < most_small_index)
                    {
                        var delta = i + (n - most_small_index);
                        a[i] -= delta;
                    }
                    else
                    {
                        var delta = i - most_small_index;
                        a[i] -= delta;
                    }

                    if (a[i] < 0)
                    {
                        Console.WriteLine("NO");
                        return;
                    }

                    if (a[i] < next_small)
                    {
                        next_small = a[i];
                        next_small_index = i;
                    }

                    if (is_finished && i != 0 && a[i] != a[i - 1])
                        is_finished = false;
                }

                if (a[0] != a[n - 1])
                    is_finished = false;

                if (is_finished)
                {
                    Console.WriteLine("YES");
                    return;
                }

                most_small_index = next_small_index;
            }
        }
    }
}