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: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
//import java.util.Scanner;

public class Main{
    public static void main(String[] args)throws Exception {
    int N =0 ,i=0,max=0,count=0;
  //  Scanner in = new Scanner (System.in);
    BufferedReader in=new BufferedReader( new InputStreamReader(System.in));
    N=Integer.parseInt(in.readLine());
   StringTokenizer x= new StringTokenizer(in.readLine());
    PrintWriter out = new PrintWriter(System.out);
  
    in.close();
    int []nthn=new int[N];
    while(N!=0){
     nthn[i]=Integer.parseInt(x.nextToken()); i++;  
     
    N--;}
    int l=nthn.length;
        for (int j = 0; j < l*2; j++) {
         //   if (j<nthn.length) System.out.print(nthn[j]+" " );
               for (int k = 0; k < l; k++) {
                   if (j<l)
                count = (nthn[j]==(nthn[k]+1)||nthn[j]==(nthn[k])-1)?++count:count;
                else
                count = ((nthn[j-l]-1)==(nthn[k]+1))?++count:count;      
            }
            max=(max>count)?max:count;
            count=0;
        }
       out.println(max+1);
       out.flush();
       out.close();
    }
}
/*

Problem Statement

You are given an integer sequence of length N, a1,a2,…,aN.

For each 1≤i≤N, you have three choices: add 1 to ai, subtract 1 from ai or do nothing.

After these operations, you select an integer X and count the number of i such that ai=X.

Maximize this count by making optimal choices.
Constraints

    1≤N≤105
    0≤ai<105(1≤i≤N)
    ai is an integer.




*/