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;
class Hello
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var a = Console.ReadLine().Split().Select(int.Parse).ToArray();
        
        var aPlus1 = a.Select(e =>e + 1);
        var aMinus1 = a.Select(e => e - 1);
        var allA = a.Concat(aPlus1.Concat(aMinus1));
        var group = allA.GroupBy(e => e).Select(e => new { e.Key, Count = e.Count() });        
        var ans = group.OrderByDescending(e => e.Count).First();


        Console.WriteLine(ans.Count);
    }
    
}