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.*;

public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);
    Map<Integer, Integer> seen = new HashMap<>();
    
    int count = scanner.nextInt();
    for (int ix = 0; ix < count; ix++) {
      int value = scanner.nextInt();
      seen.put(value - 1, seen.getOrDefault(value - 1, 0) + 1);
      seen.put(value, seen.getOrDefault(value, 0) + 1);
      seen.put(value + 1, seen.getOrDefault(value + 1, 0) + 1);
    }
 
    int maximum = 0;
    for (Map.Entry<Integer, Integer> entry : seen.entrySet()) {
      maximum = Math.max(maximum, entry.getValue()); 
    }
    
    System.out.println(maximum);
  }
}