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: Time Limit Exceeded)

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

namespace abc072
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            int[] a = new int[N];
            int ans = 0;
            string[] str = Console.ReadLine().Split(' ');
            for(int k = 0; k < N; k++)
            {
                a[k] = int.Parse(str[k]);
            }
            Array.Sort(a);
            int i = 0;
            int j = 0;
            while (i < N)
            {
                int temp = 0;
                for (int k = 0; k + i < N; k++)
                {
                    if (a[i + k] - a[i] == 1 && j == i)
                    {
                        j = i + k;
                        temp++;
                    }else if (a[i + k] - a[i] <= 2)
                    {
                        temp++;
                    }else
                    {
                        break;
                    }
                }
                ans = Math.Max(ans, temp);
                if (i == j)
                {
                    i++;
                    j++;
                }else
                {
                    i = j;
                }
            }
            Console.WriteLine(ans);
        }
    }
}