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;

public class Hello
{
    public static void Main()
    {
        var a = new int[100001];
        var n = int.Parse(Console.ReadLine().Trim());
        var amax = -1;
        string[] line = Console.ReadLine().Trim().Split(' ');
        for (int i = 0; i < n; i++)
        {
            var w = int.Parse(line[i]);
            a[w]++;
            amax = Math.Max(amax, w);
        }
        if (amax == 0) { Console.WriteLine(a[0]); goto end; }
        if (amax == 1) { Console.WriteLine(a[0] + a[1]); goto end; }
        var res = -1;
        for (int i = 0; i <= amax - 2; i++)
            res = Math.Max(res, a[i] + a[i + 1] + a[i + 2]);
        Console.WriteLine(res);
        end:;
    }
}