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;
using System.Collections.Generic;
using static System.Math;
using Debug = System.Diagnostics.Debug;

class P
{
    static void Main()
    {
        long n = int.Parse(Console.ReadLine());
        var a = Console.ReadLine().Split().Select(long.Parse).ToList();
        var sum = a.Sum();
        var incr = n * (n + 1) / 2;
        if (sum % incr != 0) goto invalid;
        var operationCount = sum / incr;
        var diffs = a.Zip(a.Skip(1), (x, y) => y - x).Concat(Enumerable.Repeat(a.First() - a.Last(), 1)).ToList();
        long totalOperate = 0;
        foreach (var diff in diffs)
        {
            if ((operationCount - diff) < 0 || (operationCount - diff) % n != 0) goto invalid;
            totalOperate += (operationCount - diff) / n;
        }
        if (totalOperate != operationCount) goto invalid;

        Console.WriteLine("YES");
        return;
        invalid:;
        Console.WriteLine("NO");
    }
}