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;

namespace CSharpSample01
{
    

    class Program
    {

        static int[] data;

        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());

            int[] input = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

            data = new int[100000 + 1];

            int max = 0;

            for(int i = 0; i < input.Count(); i++)
            {
                data[input[i]]++;
                if(input[i] > max)
                {
                    max = input[i];
                }
            }

            /*
            for(int i = 0; i <= max; i++)
            {
                Console.WriteLine($"{i} : {data[i]}");
            }
            */

            int sum = 0;
            int ans = 0;
            
            for(int x = 0; x <= max; x++)
            {
                sum += data[x];

                if(x > 0)
                {
                    sum += data[x - 1];
                }

                if(x < max)
                {
                    sum += data[x + 1];
                }

                if(ans < sum)
                {
                    ans = sum;
                }
                sum = 0;
            }


            Console.WriteLine(ans);

        }
    }
}