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.io.IOException;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws IOException{
		Together solver = new Together();
		solver.readInput();
		solver.solve();
		solver.writeOutput();
	}

	static class Together {

		private int n;
		private int a[];
		private Scanner scanner;
		private int output;
		public Together() {
			scanner = new Scanner(System.in);
		}

		public void readInput() {
			n = Integer.parseInt(scanner.next());
			a = new int[100002];
			Arrays.fill(a, 0);
			int b;
			for(int i=0; i<n; i++) {
				b = Integer.parseInt(scanner.next());
				a[b]++;
			}
			return;
		}

		public void solve() {
			output = 0;
			int sum;
			for(int i=0; i<100000;i++) {
				sum = a[i]+a[i+1]+a[i+2];
				output = Math.max(sum, output);
			}
		}

		public void writeOutput() {
			System.out.println(output);
		}

	}

}