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.IO;
using System.Linq;
using static System.Math;
using System.Text;
using System.Threading;
using System.Globalization;
using System.Runtime.CompilerServices;
using Library;

namespace Program
{
    public static class AGC010B
    {
        static public int numberOfRandomCases = 0;
        static public void MakeTestCase(List<string> _input, List<string> _output, ref Func<string[], bool> _outputChecker)
        {
        }
        static public void Solve()
        {
            var N = NN;
            var AList = NNList(N).ToArray();
            var sa = new long[N];
            for (var i = 0; i < N; i++)
            {
                sa[i] = AList[(i + 1) % N] - AList[i];
            }
            if (sa.All(e => e == 0))
            {
                for (var i = 0; i < N; i++)
                {
                    if (AList[i] % ((N + 1) * N / 2) != 0)
                    {
                        Console.WriteLine("NO");
                        return;
                    }
                }
                Console.WriteLine("YES");
                return;
            }
            var blist = new long[N * 3];
            var b2list = new long[N * 3];
            for (var i = 0; i < N; i++)
            {
                if (sa[(i + 1) % N] < sa[i])
                {
                    if ((sa[i] - sa[(i + 1) % N]) % N == 0)
                    {
                        blist[i + 2] += (sa[i] - sa[(i + 1) % N]) / N;
                        b2list[i + 2 + N] += (sa[i] - sa[(i + 1) % N]) / N;
                        sa[(i + 1) % N] = sa[i];
                    }
                    else
                    {
                        Console.WriteLine("NO");
                        return;
                    }
                }
            }
            var added = 0L;
            var addeded = 0L;
            var clist = new long[N * 3];
            for (var i = 0; i < N * 3; i++)
            {
                added += blist[i];
                added -= b2list[i];
                addeded += added;
                addeded -= b2list[i] * N;
                clist[i] += addeded;
            }
            for (var i = 0; i < N; i++)
            {
                if ((AList[i]) != (clist[i] + clist[i + N] + clist[i + 2 * N]))
                {
                    Console.WriteLine("NO");
                    return;
                }
            }
            Console.WriteLine("YES");
        }
        static class Console_
        {
            static Queue<string> param = new Queue<string>();
            public static string NextString() { if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item); return param.Dequeue(); }
        }
        class Printer : StreamWriter
        {
            public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
            public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { base.AutoFlush = false; }
            public Printer(Stream stream, Encoding encoding) : base(stream, encoding) { base.AutoFlush = false; }
        }
        static public void Main(string[] args) { if (args.Length == 0) { Console.SetOut(new Printer(Console.OpenStandardOutput())); } var t = new Thread(Solve, 134217728); t.Start(); t.Join(); Console.Out.Flush(); }
        static long NN => long.Parse(Console_.NextString());
        static double ND => double.Parse(Console_.NextString());
        static string NS => Console_.NextString();
        static long[] NNList(long N) => Repeat(0, N).Select(_ => NN).ToArray();
        static double[] NDList(long N) => Repeat(0, N).Select(_ => ND).ToArray();
        static string[] NSList(long N) => Repeat(0, N).Select(_ => NS).ToArray();
        static IEnumerable<T> OrderByRand<T>(this IEnumerable<T> x) => x.OrderBy(_ => xorshift);
        static long Count<T>(this IEnumerable<T> x, Func<T, bool> pred) => Enumerable.Count(x, pred);
        static IEnumerable<T> Repeat<T>(T v, long n) => Enumerable.Repeat<T>(v, (int)n);
        static IEnumerable<int> Range(long s, long c) => Enumerable.Range((int)s, (int)c);
        static uint xorshift { get { _xsi.MoveNext(); return _xsi.Current; } }
        static IEnumerator<uint> _xsi = _xsc();
        static IEnumerator<uint> _xsc() { uint x = 123456789, y = 362436069, z = 521288629, w = (uint)(DateTime.Now.Ticks & 0xffffffff); while (true) { var t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); yield return w; } }
    }
}
namespace Library {
}