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.Scanner;
import java.util.Arrays;

class Main{
        public static void main(String[] args){
                Scanner scanner=new Scanner(System.in);
                int N=scanner.nextInt();
                int[] a=new int[N+1];
                for(int i=0;i<N;i++){
                        a[i]=scanner.nextInt();
                }
                a[N]=Integer.MAX_VALUE;
                Arrays.sort(a);
                a[N]=-1;

                int[][] num=new int[a.length][2];
                int n=1;
                int indexNum=0;
                for(int i=0;i<a.length-1;i++){
                        if(a[i+1]==-1){
                                num[indexNum]=new int[]{a[i],n};
                        }else{
                                if(a[i]==a[i+1]){
                                        n++;
                                }else{
                                        num[indexNum++]=new int[]{a[i],n};
                                        n=1;
                                }
                        }
                }

                int max=0;
                int sum=0;
                for(int i=0;i<num.length-2;i++){
                        if(num[i][0]==num[i+1][0]-1 && num[i+1][0]==num[i+2][0]-1){
                                sum=num[i][1]+num[i+1][1]+num[i+2][1];
                                if(max<sum){
                                        max=sum;
                                }
                        }
                }
                if(max==0){
                        for(int i=0;i<num.length-2;i++){
                                if(num[i][0]==num[i+1][0]-1 || num[i][0]==num[i+1][0]-2){
                                        sum=num[i][1]+num[i+1][1];
                                        if(max<sum){
                                                max=sum;
                                        }
                                }
                        }
                }
                if(max==0){
                        for(int i=0;i<num.length-2;i++){
                                sum=num[i][1];
                                if(max<sum){
                                        max=sum;
                                }
                        }
                }

                System.out.println(max);
        }
}