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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.IOException;
import java.util.Arrays;

public class Main {
  public static void main(String[] args) throws IOException {
    BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    int n = Integer.parseInt(in.readLine());
    int[] a = new int[n];
    String[] str = in.readLine().split(" ");
    for(int i=0; i<n; i++) {
      a[i] = Integer.parseInt(str[i]);
    }
    
    Arrays.sort(a);
    
    int max = 0;
    for(int i=0; i<n-2; i++) {
    int count = 0;
      for(int j=0; j<n-2; j++) {
        if(Math.abs(a[i]-a[j])<=1) {
          count++;
        } else {
          max = Math.max(count,max);
          break;
        }
      }
    }
    System.out.println(n==1?"1":max);
  }
}