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.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner reader = new Scanner(System.in);
		int N = reader.nextInt();
		int ans = 0;
		int min = 100000;
		int max = 0;
		int[] all = new int[100001];
		int[] arr = new int[N];
		for (int i = 0; i < N; i++) {
			arr[i] = reader.nextInt();
			all[arr[i]]++;
			min = Math.min(min, arr[i]);
			max = Math.max(max, arr[i]);
		}
		for (int i = min; i <= max; i++) {
			int tmp = all[i];
			if (i > 0) {
				tmp += all[i-1];
			}
			if (i < 100000) {
				tmp += all[i+1];
			}
			ans = Math.max(tmp, ans);
		}

		System.out.println(ans);
		reader.close();

	}
}