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: Time Limit Exceeded)

import java.util.*;

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> integers = new ArrayList<>();
        ArrayList<Integer> x = new ArrayList<>();
        ArrayList<Integer> numOfX = new ArrayList<>();

        for (int i = 0; i < N; i++) {
            integers.add(Integer.parseInt(scanner.next()));
        }
        integers.sort(Comparator.naturalOrder());

        int count = 1;
        x.add(integers.get(0));
        for (int i = 1; i < N; i++) {
            if (!x.contains(integers.get(i))) {
                x.add(integers.get(i));
                numOfX.add(count);
                count = 1;
            } else {
                count++;
            }
        }
        numOfX.add(count);

//        for (int i = 0; i < x.size(); i++) {
//            System.out.print(x.get(i) + ":");
//            System.out.println(numOfX.get(i));
//        }

        int answer = 0;

        for (int i = 0; i < x.size(); i++) {
            for (int j = -1; j < 2; j++) {

                int tmp = 0;
                int X = x.get(i) + j;

                if (x.contains(X)) {
                    tmp += numOfX.get(x.indexOf(X));
                }
                if (x.contains(X-1)) {
                    tmp += numOfX.get(x.indexOf(X-1));
                }
                if (x.contains(X+1)) {
                    tmp += numOfX.get(x.indexOf(X+1));
                }

                if (tmp > answer) {
                    answer = tmp;
                }
            }
        }

        System.out.println(answer);
    }
}