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

namespace atcorder2
{
    class Program
    {
        public static long Read()
        {
            return long.Parse(Console.ReadLine());
        }

        public static long[] Reads()
        {

            return Console.ReadLine().Split().Select(long.Parse).ToArray();
        }






        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);


            var n = Read();
            var a = Reads();
            var count = new long[(long)Math.Pow(10,5)+1];
            for (int i = 0; i < n; i++)
            {
                count[a[i]]++;
            }
            long ans = 0;
            for (int i = 0; i <= (long)Math.Pow(10,5)-2; i++)
            {
                var tmp = count[i] + count[i + 1] + count[i + 2];
                ans = Math.Max(tmp, ans);
            }
            Console.WriteLine(ans);
         
            Console.Out.Flush();
        }
    }
}