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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ

		Scanner sc = new Scanner(System.in);
		int N=sc.nextInt();
		int a[]=new int[N];
		for(int i=0;i<N;i++) {
			a[i]=sc.nextInt();
		}
		Arrays.sort(a);
		int c[]=new int[100001];
		int i=0;int j=0;int k=0;
		while(j<N) {
			while(j<N&&k==a[j]) {
				i++;j++;
			}
			c[k]=i;
			k++;
			i=0;
		}
		int d[]=new int[99999];
		int x=0;
		for(int l=0;l<99999;l++) {
			d[l]=c[l]+c[l+1]+c[l+2];
			if(x<d[l])x=d[l];
		}

		System.out.println(x);
	}
}