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.Linq;
public class Hello{
    public static void Main(){
        var n = int.Parse(Console.ReadLine());
        var array = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        var memo = new int[100002];
        var max = 0;
        var dx = new int[]{-1,0,1};
        for(var i = 0;i < n;i++){
            for(var j = 0;j < 3;j++){
                if(array[i] + dx[j] > 0) memo[array[i] + dx[j]]++; 
            }
        }
        
        Console.WriteLine(memo.Max());
        
    }
}