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.*;
import static java.lang.System.*;

class Main {
  public static final int MOD = 1000000007;
  public static final int INF = 1000000000;
  public static void main(String[] args) {
    Scanner sc = new Scanner(in);
    int N = sc.nextInt();
    int count[] = new int[100010];
    Arrays.fill(count, 0);
    for(int i=0; i<N; i++){
      int a = sc.nextInt();
      count[a]++;
    }
    int ans = 0;
    for(int i=0; i<count.length-2; i++){
      int tmp = count[i] + count[i+1] + count[i+2];
      ans = Math.max(ans, tmp);
    }
    out.println(ans);
  }

  public static int gcd(int a, int b){
    if(b == 0) return a;
    return gcd(b, a%b);
  }
}