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.HashMap;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		try (Scanner sc = new Scanner(System.in)) {
			int n = sc.nextInt();
			HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();

			for (int i = 0; i < n; i++) {
				int a = sc.nextInt();
				if (map.containsKey(a)) {
					map.put(a, map.get(a) + 1);
				} else {
					map.put(a, 1);
				}

				if (map.containsKey(a - 1)) {
					map.put(a - 1, map.get(a - 1) + 1);
				} else {
					map.put(a - 1, 1);
				}

				if (map.containsKey(a + 1)) {
					map.put(a + 1, map.get(a + 1) + 1);
				} else {
					map.put(a + 1, 1);
				}
			}

			int max = 0;
			for (int i : map.keySet()) {
				if (max < map.get(i)) {
					max = map.get(i);
				}
			}

			System.out.println(max);
		}
	}
}