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.Scanner;
import java.util.Arrays;

public class Main{
  public static void main(String[] args){
    Scanner scanner = new Scanner(System.in);
    int N = scanner.nextInt();
    int[] a = new int[N];
    int count = 0;
    int ans = 0;
    for (int i = 0; i < N; i++){
      a[i] = scanner.nextInt();
    }
    for (int i = 0; i < N; i++){
      for (int j = 0; j < N; j++){
        if (a[i] == a[j]) {
          count++;
        } else if (a[i] == a[j] - 1){
          count++;
        } else if (a[i] == a[j] + 1){
          count++;
        }
        ans = Math.max(count, ans);
      }
      count = 0;
    }
    System.out.println(ans);
  }
}