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.Text;
using static System.Convert;
using static System.Console;
using static System.Math;
class MainClass
{
	static void Main(string[] args)
	{
		Answer();
	}
	public static void Answer()
	{
      var n = int.Parse(Console.ReadLine());
      var list = Console.ReadLine().Split(' ').Select(int.Parse).ToList();

      var dicNumandCnt = new Dictionary<int, int>();
      foreach(var a in list)
      {
        for (int i = a - 1; i <= a+1; i++)
        {
          if (dicNumandCnt.ContainsKey(i))
          {
            dicNumandCnt[i]++;
          }
          else
          {
            dicNumandCnt.Add(i, 1);
          }
        }
      }
      Console.WriteLine(dicNumandCnt.Values.Max());
	}
}