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;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Diagnostics;

namespace ConsoleApplication
{
    class Program
    {
        static void Main()
        {
            new Solution().answer();
        }
    }

    class Solution
    {
        string N, M, T;
        public Solution()
        {
            N = Console.ReadLine();
            M = Console.ReadLine();
            int j = Convert.ToInt32(N);
            string[] M_split = new string[j];
            string[] M_split_full = new string[j * 3];

            M_split = M.Split(' ');
            int a;
            for (a = 0; a < j; a++)
            {
                M_split_full[a] = M_split[a];
                M_split_full[j + a] = (Convert.ToInt32(M_split[a]) - 1).ToString();
                M_split_full[(2 * j) + a] = (Convert.ToInt32(M_split[a]) + 1).ToString();
            }

            var count =(from item in M_split_full
                        group item by item into g
                        select g.Count()).ToList();

            var ans = (from item in count
                       group item by item into g
                       select g.Max()).ToList();

            ans.Sort();
            T = ans[ans.Count() - 1].ToString();                          
        }

        public void answer()
        {
            Console.WriteLine(T);
        }
    }
}