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: Accepted)


import java.util.Arrays;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
	Main m = new Main();
	m.answer();
    }

    private Scanner scan = new Scanner(System.in);
    private static final int MAX = 100000;
    private final int[] count;

    public Main() {
	count = new int[MAX+1];
	
	int N = Integer.parseInt(scan.next());
	for (int i = 0; i < N; i++) {
	    int a = Integer.parseInt(scan.next());
	    count[a]++;
	}

	scan.close();
    }

    public final void answer() {
	int[] result = new int[MAX+1];
	for (int i = 0; i <= MAX; i++) {
	    result[i] =  count[i];
	    if(i > 0) result[i] += count[i-1];
	    if(i < MAX) result[i] += count[i+1];
	}

	Arrays.sort(result);
	System.out.println(result[MAX]);
    }
}