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)

//#pragma warning disable

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

public class Test
{
    public static void Main()
    {
        var N = long.Parse(Console.ReadLine());

        var a = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();

        var nums = new long[100010];  // 最初は -1, 最後が 10001

        foreach (var x in a)
        {
            nums[x + 1]++;
        }

        long max = 0;

        for (int i = 0; i < nums.Length - 2; i++)
        {
            max = Math.Max(max, nums[i] + nums[i + 1] + nums[i + 2]);
        }

        Console.WriteLine(max);

    }
}