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;
using System.Collections.Generic;

namespace atCoder
{
    class Program
    {
        static void Main()
        {
            int n = int.Parse(Console.ReadLine());
            string[] temp = Console.ReadLine().Split(' ');
            List<int> a = new List<int>();

            for (int i = 0; i < n; i++)
            {
                a.Add(int.Parse(temp[i]));
            }

            a.Sort();

            int result = 0;

            for (int i = a[0]; i <= a[a.Count - 1] + 1; i++)
            {
                int count = 0;

                for (int j = 0; j < n; j++)
                {
                    if (a[j] < i - 1) continue;
                    if (i + 1 < a[j]) break;

                    int b;

                    if (i < a[j])
                    {
                        b = a[j] - 1;
                    }
                    else if (a[j] < i)
                    {
                        b = a[j] + 1;
                    }
                    else
                    {
                        b = a[j];
                    }

                    if (i == b)
                    {
                        count++;
                    }
                }

                if (result < count)
                {
                    result = count;
                }
            }

            Console.WriteLine(result);
        }
    }
}