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.ArrayList;
import java.util.Comparator;
import java.util.Scanner;

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

        int N = scanner.nextInt();

        if (N == 1) {
            System.out.println("1");
            return;
        }

        ArrayList<Integer> a = new ArrayList<>();

        for (int i = 0; i < N; i++) {
            a.add(Integer.parseInt(scanner.next()));
        }

        a.sort(Comparator.reverseOrder());

        int count = 1;
        int maxCount = 1;
        int zeroCount = 1;
        int before = -1;


        for (int i = 0; i < N - 1; i++) {
            int tmp = a.get(i) - a.get(i+1);

            if (tmp == 1) {
                if (before == 1) {
                    count = 3;
                } else if (before == 0) {
                    count++;
                } else {
                    count = 2;
                }
            } else if (tmp == 0) {
                count++;
                zeroCount ++;
            } else if (tmp == 2 && before == 0) {
                count = zeroCount + 1;
                zeroCount = 1;
            } else  {
                count = 1;
            }

            if (count > maxCount) {
                maxCount = count;
            }

            before = tmp;
//            System.out.println(count);
        }

        System.out.println(maxCount);
    }
}