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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
class Program
{
    private int[] GetMinMax(int[] num)
    {
        int min = 100000;
        int max = 0;
        for (int i = 0; i < num.Length; i++)
        {
            if (num[i] < min)
                min = num[i];
            if (num[i] > max)
                max = num[i];
        }
        int[] minmax = { min, max };
        return minmax;
    }
    private int Count(int[] num, int k)
    {
        int c = 0;
        for (int i = 0; i < num.Length; i++)
            if (num[i] == k - 1 || num[i] == k || num[i] == k + 1)
                c++;
        return c;
    }
    public static void Main()
    {
        Program prog = new Program();
        int n = int.Parse(Console.ReadLine());
        string[] str = Console.ReadLine().Split(' ');
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = int.Parse(str[i]);
        int min, max;
        int[] minmax = prog.GetMinMax(a);
        min = minmax[0];
        max = minmax[1];
        int t = 0;
        for (int i = min; i <= max; i++)
        {
            if (prog.Count(a, i) > t)
                t = prog.Count(a, i);
        }
        Console.WriteLine(t);
    }
}