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

namespace AtCoderGrandContest010
{
    class ProgramB
    {
        private const string kYes = "YES";
        private const string kNo = "NO";
        static void Main(string[] args)
        {
            string szTotal = Console.ReadLine();
            int nTotal = int.Parse(szTotal);
            long[] arr = new long[nTotal];

            string szLine = Console.ReadLine();
            string[] szSplittedLine = szLine.Split(' ');

            for (int i = 0; i < szSplittedLine.Length; ++i)
            {
                long a = long.Parse(szSplittedLine[i]);
                arr[i] = a;
            }
            string ret = Solve(arr) ? kYes : kNo;
            Console.WriteLine(ret);
        }

        private static bool Solve(long[] arr)
        {
            long nTotal = arr.Length;
            long nStoneTotal = 0;// 石総数
            for (int i = 0; i < arr.Length; ++i)
            {
                nStoneTotal += arr[i];
            }

            long nSubTotal = (nTotal * (nTotal + 1)) / 2;// 一回の操作で除かれる石

            if (nStoneTotal % nSubTotal != 0) { return false; ; }
            long step = nStoneTotal / nSubTotal;// K回で終わる

            // 配列を変換し、問題をすり替える
            long[] arr_custom = new long[nTotal];
            for (int i = 0; i < arr_custom.Length; ++i)
            {
                long dt = arr[(i + 1) % nTotal] - arr[i];
                arr_custom[i] = dt - step;
            }

            // 各数字は N の倍数か？ K回のNの加算で解決できるぁ？
            long nAddTotal = 0;
            for (int i = 0; i < arr_custom.Length; ++i)
            {
                long dt = arr_custom[i];
                if (dt > 0) { return false; }
                if( dt == 0) { continue; }
                if (Math.Abs(dt) % nTotal != 0) { return false; }
                nAddTotal += Math.Abs( dt) / nTotal;
            }
            if( nAddTotal != step) { return false; }
            return true;
        }
    }
}