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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC072_C
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var input = Console.ReadLine().Split(' ');
            var a = new List<int>();
            for (int i = 0; i < N; i++)
            {
                a.Add(int.Parse(input[i]));
            }
            a.Sort();
            var maxCount = 0;
            var countHitNum = 0;
            for (int i = 0; i <= a[a.Count - 1]; i++)
            {
                if (a.BinarySearch(i) >= 0 || a.BinarySearch(i - 1) >= 0 || a.BinarySearch(i + 1) >= 0)
                {
                    var count = 0;
                    
                    for (int j = a.IndexOf(countHitNum) - 3; j < N; j++)
                    {
                        if (j < 0)
                        {
                            continue;
                        }
                        if (i + 1 >= a[j] && i - 1 <= a[j])
                        {
                            count++;
                            countHitNum = a[j];
                        }
                        if (j - 2 == countHitNum)
                        {
                            break;
                        }
                    }
                    if (maxCount < count)
                    {
                        maxCount = count;
                    }
                }
            }


            Console.WriteLine(maxCount);
        }


    }
}