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.*;

class Main {
    public static void main(String[] args) {
        new Solver().run();
    }
}

class Solver {

    public void run() {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] a = new int[N];

        int max = Integer.MIN_VALUE;
        for (int i = 0; i < N; i++) {
            a[i] = sc.nextInt();
            max = Math.max(max, a[i]);
        }

        int[] cnt = new int[max + 3];
        for (int i = 0; i < N; i++) {
            cnt[a[i] + -1 + 1]++;
            cnt[a[i] +  0 + 1]++;
            cnt[a[i] +  1 + 1]++;
        }

        int ans = Integer.MIN_VALUE;
        for (int i = 0; i < max + 2; i++) {
            ans = Math.max(ans, cnt[i]);
        }

        System.out.println(ans);
        return;
    }

}