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.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace ProCon
{

    class Program
    {
        static void Main(string[] args)
        {
            Console.ReadLine();
            string[] input = Console.ReadLine().Split(' ');
            List<int> nums = new List<int>();
            for (int i = 0; i < input.Count(); ++i)
            {
                nums.Add( int.Parse(input[i]) );
            }
            nums.Sort();
            int b = -1;
            int maxNum = 0;
            for( int i = 0; i < input.Count(); ++i)
            {
                if( b == nums[i])
                {
                    continue;
                }
                b = nums[i];
                int res = 1;
                for( int x = i + 1; x < input.Count(); ++x)
                {                   
                    if ( nums[x] >= b + 3 )
                    {
                        break;
                    }
                    res++;
                }
                if(res > maxNum)
                {
                    maxNum = res;
                }
            }
            Console.WriteLine(maxNum);
        }
    }

}