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.*;

// ARC 82-C
// https://beta.atcoder.jp/contests/arc082/tasks/arc082_a

public class Main {

	public static void main (String[] args) {
		Scanner in = new Scanner(System.in);
		
		int N = in.nextInt();

		HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
		
		for (int i = 0; i < N; i++) {
			int n = in.nextInt();
			
			if (map.containsKey(n - 1)) {
				int count = map.get(n - 1);
				map.put(n - 1, count + 1);
			} else {
				map.put(n - 1, 1);
			}
			if (map.containsKey(n)) {
				int count = map.get(n);
				map.put(n, count + 1);
			} else {
				map.put(n, 1);
			}
			if (map.containsKey(n + 1)) {
				int count = map.get(n + 1);
				map.put(n + 1, count + 1);
			} else {
				map.put(n + 1, 1);
			}
		}
		
		int answer = 0;
		
		for (int k : map.keySet()) {
			answer = Math.max(answer, map.get(k));
		}
		
		System.out.println(answer);
	}
}