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 sc = new Scanner(System.in);
    int n = sc.nextInt();
    int[] a = new int[n];
    for(int i = 0; i < n; i++) {
      a[i] = sc.nextInt();
    }
    Arrays.sort(a);
    int pos = 0;
    int[] b = new int[n];
    for(int i = 0; i < n; i++) {
      if(a[pos] + 2 >= a[i]) {
      } else {
        b[pos] = i - pos;
        pos++;
        i--;
      }
    }
    if(b[0] == 0) b[0] = n; 
    int ans = 0;
    for(int i = 0; i < n; i++) {
      ans = Math.max(ans, b[i]);
    }
    if(n > 1) {
      System.out.println(ans);
    } else {
      System.out.println(1);
    }
  }
}