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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        ArrayList<Integer> a = new ArrayList<>();
        for (int i=0;i<n;i++){
            a.add(scanner.nextInt());
        }
        ArrayList<Integer> b = new ArrayList<>();
        for (int i=0;i<n;i++){
            b.add(a.get(i)-1);
            b.add(a.get(i));
            b.add(a.get(i)+1);
        }
        int max = 0;
        for (int i:new LinkedHashSet<>(b)){
            int count = 0;
            for (int j:b){
                if (i==j){
                    count++;
                }
            }
            if (count>max){
                max = count;
            }
        }
        System.out.println(max);
    }

}