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: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;


public class Main {

	/**
	 * @param args
	 * @throws IOException 
	 * @throws NumberFormatException 
	 */
	public static void main(String[] args) throws NumberFormatException, IOException {
		// TODO Auto-generated method stub
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		
		int n = Integer.parseInt(br.readLine());
		

		
		String[] tmpArray = br.readLine().split(" ");
		
		int[] input = new int[n];
		int[] index = new int[100001];
		Arrays.fill(index, -1);
		
		for(int i = 0; i < n; i++){
			input[i] = Integer.parseInt(tmpArray[i]);
		}
		
		Arrays.sort(input);
		if(n == 1){
			System.out.println(1);
			return;
		}		
		if(n == 2){
			if(input[1] - input[0] <= 2){
				System.out.println(2);
			}
			else {
				System.out.println(1);
			}
			return;
		}
		
		for(int i = 0; i < input.length ; i++){
			if(index[input[i]] == -1){
				index[input[i]] = i;
			}
		}
		
		for(int i = 1; i < index.length; i++){
			if(index[i] == -1 && index[i - 1] >= 0){
				index[i] = index[i - 1];
			}
		}
		
		int max = 0;
		for(int i = 1; i < index.length - 2 ; i++){
			if(index[i + 2] - index[i] + 1 > max){
				max = index[i + 2] - index[i] + 1;
			}
		}
		
		System.out.println(max);
	}

}