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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;

namespace cs
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(ReadLine());
            var line = ReadLine()
                .Split(' ')
                .Select(_ => int.Parse(_))
                .GroupBy(_ => _)
                .ToDictionary(_ => _.Key, __ => __.Count())
                ;
            int result = 0;
            foreach (var num in line)
            {
                int value = num.Value;
                if (line.ContainsKey(num.Key - 1))
                    value += line[num.Key - 1];
                if (line.ContainsKey(num.Key + 1))
                    value += line[num.Key + 1];
                if(result < value)
                    result = value;
            }
            WriteLine(result);
            ReadLine();
        }
    }
}