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: Accepted)

import java.util.Scanner;
import java.util.TreeMap;

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

    int N = scanner.nextInt();
    TreeMap<Integer, Integer> count = new TreeMap<>();
    for (int i = 0; i < N; i++) {
      int a = scanner.nextInt();
      count.put(a, count.getOrDefault(a, 0) + 1);
    }

    Integer[] keys = count.keySet().toArray(new Integer[0]);
    int num = count.get(keys[0]);
    for (int i = 1; i < keys.length; i++) {
      int c = count.get(keys[i]);
      if (keys[i - 1] + 1 == keys[i])
        c += count.get(keys[i - 1]);
      if (i < keys.length - 1 && keys[i + 1] == keys[i] + 1)
        c += count.get(keys[i + 1]);
      num = Math.max(num, c);
    }
    System.out.println(num);
  }
}