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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
 
public class Main {  
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    int[] a = new int[N];
    int[] count = new int[100001];
    int amax =0, amin =10000;
    for (int i =0; i<N; i++) {
      a[i] = sc.nextInt();
      amax = Math.max(a[i],amax);
      amin = Math.min(a[i],amin);
      count[a[i]]++;
    }
    int max =0;
    for (int i =Math.max(0,amin-2); i<=amax-2; i++) {
      max = Math.max(count[i] + count[i+1] + count[i+2],max);
    }
    System.out.println(max);  
  }
}