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;

class Program
{
    static void Main(string[] args)
    {
        var n = int.Parse(Console.ReadLine());
        var s = Console.ReadLine().Split(' ');

        var dict = new Dictionary<int, int>();
        var dx = new[] { -1, 0, 1 };
        for (int i = 0; i < n; i++)
        {
            var x = int.Parse(s[i]);
            for (int j = 0; j < 3; j++)
            {
                var sx = x + dx[j];
                if (dict.ContainsKey(sx))
                {
                    dict[sx]++;
                }
                else
                {
                    dict[sx] = 1;
                }
            }
        }

        var ans = 0;
        foreach (var item in dict)
        {
            ans = Math.Max(ans, item.Value);
        }
        Console.WriteLine(ans);
    }
}