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;

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

		int n = sc.nextInt();
		int[] a = new int[n];
		int[] cnt = new int[100000];
		int[] around = new int[100000];

		for(int i=0; i<100000; i++){
			cnt[i] = 0;
			around[i] = 0;
		}


		for(int i=0; i<n; i++){
			a[i] = sc.nextInt();
			cnt[a[i]]++;
			around[a[i]]++;
			if(a[i]!=0){
				around[a[i]-1]++;
			}
			if(a[i]!=99999){
				around[a[i]+1]++;
			}
		}

		int maxIdx=0;
		int max=around[0];
		for(int i=1; i<n; i++){
			if(around[i]>max){
				maxIdx=i;
				max=around[i];
			}
		}
		if(maxIdx-2>=0){
			if(around[maxIdx]==around[maxIdx-2]){
				max--;
			}
		}
		if(maxIdx+2<=99999){
			if(around[maxIdx]==around[maxIdx+2]){
				max++;
			}
		}

		System.out.print(max);
	}
}