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;

class Main{
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);

		int input=sc.nextInt();
		int[] suji=new int[100001];

		for(int i=0; i<100001; i++) {
			suji[i]=0;
		}

		for(int i=0; i<input; i++) {
			suji[sc.nextInt()]++;
		}

		int[] wa=new int[100003];
		wa[0]=suji[0];		//-1
		wa[1]=suji[0]+suji[1];	//0
		wa[100001]=suji[99999]+suji[100000];	//100000
		wa[100002]=suji[100000];		//100001

		for(int i=2; i<=100000; i++) {
			wa[i]=suji[i-2]+suji[i-1]+suji[i];
		}

		int max=0;
		for(int i=0; i<=100002; i++) {
			if(max<wa[i]) {
				max=wa[i];
			}
		}

		System.out.println(max);
	}
}