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.*;

public class Main {
    
  public static void main(String[] args) {
   
      Scanner sc = new Scanner(System.in);                      
               
      int N = sc.nextInt();
     
      int max = Integer.MIN_VALUE;
      
      int a[] = new int[N];
      
      for(int i = 1 ;i <= N;i++){
          int c = sc.nextInt();
          a[i-1] = c;
          if(c > max){
              max = c;
          }
      }
      
      int count[] = new int[max+2];
            
      for(int i = 0;i < N;i++){
          if(a[i] == 0){
              count[a[i]]++;
              count[a[i]+1]++;
          }else{
              count[a[i]-1]++;
              count[a[i]]++;
              count[a[i]+1]++;
          }
      }      
      
      int ans = Integer.MIN_VALUE;
      
      for(int i = 0;i < max+2;i++){
          if(count[i] > ans){
              ans = count[i];
          }          
      }
      
      System.out.println(ans);
     
      
  }                
}