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;
using System.Linq;
using System.Linq.Expressions;
using System.IO;
using System.Text;
using System.Diagnostics;

class Program
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        int[] a = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        Dictionary<int, int> map = new Dictionary<int, int>();

        for (int i = -1; i < 100002; i++)
        {
            map[i] = 0;
        }

        for (int i = 0; i < n; i++)
        {
            if (map.ContainsKey(a[i])) {
                map[a[i]]++;
            }
            else
            {
                map[a[i]] = 1;
            }
        }

        long ans = map.Values.Max();

        for(int i = 0; i < n; i++)
        {
            ans = Math.Max(ans, map[i - 1] + map[i] + map[i + 1]);
        }

        Console.WriteLine(ans);
    }
}