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 Java (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

class Main
{
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    int[] A = new int[N];
    int[] freq = new int[(int)1e5 + 1];
    //10^5 = 100,000
    //~2e9
    for (int i = 0; i < N; i++)
    {
      A[i] = sc.nextInt();
    }
    for (int i = 0; i < N; i++)
    {
      freq[A[i]] += 1; //case do nothing:
      if (A[i] - 1 >= 0) freq[A[i] - 1] += 1;
      freq[A[i] + 1] += 1;
    }
    int count = 0;
    for (int i = 0; i< 1e5 + 1; i++)
    {
      count = Math.max(count, freq[i]);
    }
    System.out.println(count);
  }
}