Problem:
Score : 300 points

Problem Statement

You are given an integer sequence of length N, a_1,a_2,...,a_N.

For each 1≤i≤N, you have three choices: add 1 to a_i, subtract 1 from a_i or do nothing.

After these operations, you select an integer X and count the number of i such that a_i=X.

Maximize this count by making optimal choices.

Constraints

1≤N≤10^5

0≤a_i<10^5 (1≤i≤N)

a_i is an integer.

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 .. a_N

Output

Print the maximum possible number of i such that a_i=X.

Sample Input 1

7
3 1 4 1 5 9 2

Sample Output 1

4

For example, turn the sequence into 2,2,3,2,6,9,2 and select X=2 to obtain 4, the maximum possible count.

Sample Input 2

10
0 1 2 3 4 5 6 7 8 9

Sample Output 2

3

Sample Input 3

1
99999

Sample Output 3

1

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

namespace arc082_a
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = GetInt();
            var AL = GetIntList();
            var AD = new Dictionary<int, int>();
            foreach (var a in AL)
            {
                if (!AD.ContainsKey(a - 1)) AD.Add(a - 1, 0);
                if (!AD.ContainsKey(a)) AD.Add(a, 0);
                if (!AD.ContainsKey(a + 1)) AD.Add(a + 1, 0);
                AD[a - 1]++;
                AD[a]++;
                AD[a + 1]++;
            }
            Console.WriteLine(AD.Values.Max());
        }

        public static string GetStr() => Console.ReadLine();
        public static int GetInt() => int.Parse(Console.ReadLine());
        public static long GetLong() => long.Parse(Console.ReadLine());
        public static double GetDouble() => double.Parse(Console.ReadLine());
        public static decimal GetDecimal() => decimal.Parse(Console.ReadLine());

        public static List<string> GetStrList() => Console.ReadLine().Split(' ').ToList();
        public static List<int> GetIntList() => Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToList();
        public static List<long> GetLongList() => Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList();
        public static List<double> GetDoubleList() => Console.ReadLine().Split(' ').Select(x => double.Parse(x)).ToList();
        public static List<decimal> GetDecimalList() => Console.ReadLine().Split(' ').Select(x => decimal.Parse(x)).ToList();

    }
}