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.*;

class Main{
    public static void main(String[]args){
		Scanner sc = new Scanner(System.in);
		int iin = sc.nextInt();
		int iis = 0;
		int iism = 0;
		int iimm = 0;
		int irt = 0;
		TreeMap<Integer,Integer> ihm = new TreeMap<Integer,Integer>();
		for(int i=0;i<iin;i++){
			iis = sc.nextInt();
			if(iis<iism || i==0){
				iism = iis;
			}
			if(iis>iimm || i==0){
				iimm = iis;
			}
			if(ihm.containsKey(iis)){
				int iat = ihm.get(iis);
				iat++;
				ihm.put(iis, iat);
			}
			else{
				ihm.put(iis, 1);
			}
		}
		for(int i=iism;i<=iimm;i++){
			iis = 0;
			if(ihm.containsKey(i-1)){
				iis += ihm.get(i-1);
			}
			if(ihm.containsKey(i)){
				iis += ihm.get(i);
			}
			if(ihm.containsKey(i+1)){
				iis += ihm.get(i+1);
				iism = i + 1;
			}
			if(irt<iis){
				irt = iis;
			}
			else if(iis==0){
				i = ihm.higherKey(i) - 1;
			}
		}
		System.out.println(irt);
    }
}