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: Wrong Answer)

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

		int N = sc.nextInt();
		int[] A = new int[N+1];
		for( int i=1; i<=N; i++ ){
			A[i] = sc.nextInt();
		}
		Arrays.sort(A);
		A[0] = 100004;      
		int count = 1;
		int a = N;
		int b = N-1;
		int ans = 0;
		int n = 0;
		for( int i=0; i<N-1; i++ ){            
			if( A[a] - A[b] >2 ){
				a--;
				b--;     
				if( a<2 ){
					break;                  
                }                  
            }              
			if( A[a] - A[b] <=2 ){              
				count++;
				b--;           
				if( Math.abs(A[a] - A[b]) >2 ){
					ans = Math.max(ans,count);               
					count = 1;
					a = b+1;
					b = a-1;
				}
				if( a<2 ){
					break;                  
                }                  
			}
		}      
		if( N==1 || ans==0 ){
			ans = 1;          
        }          
		System.out.println(ans);
	}
}