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;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var p = new Program();
            p.Solve();
        }

        void Solve()
        {
            int n = int.Parse(Console.ReadLine());
            var a = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
            Array.Sort(a);

            int maxCount = 1;
            int count = 1;
            int preCount = -1;
            int prepreCount = -1;
            int current = a[0];
            for (int i = 1; i < a.Length; i++)
            {
                if (a[i] == current)
                {
                    count++;
                }
                else
                {
                    int c;
                    if (preCount == -1)
                    {
                        c = count;

                    }
                    else if (prepreCount == -1)
                    {
                        c = count + preCount;
                    }
                    else
                    {
                        c = count + preCount + prepreCount;
                    }
                    maxCount = Math.Max(maxCount, c);
                    prepreCount = preCount;
                    preCount = count;


                    current = a[i];
                    count = 1;
                }
            }
            Console.WriteLine(maxCount);

        }

    }
}