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

class Program
{
    static void Main(string[] args)
    {
        // 入力
        var n = long.Parse(Console.ReadLine());
        long[] a =  Console.ReadLine().Split().Select(long.Parse).ToArray();

        var dic = new Dictionary<long, long>() { };
        for (int i = 0; i < n; i++)
        {
            if (!dic.ContainsKey(a[i]))
            {
                dic.Add(a[i], 1);
            }
            else
            {
                dic[a[i]]++;
            }

            if (!dic.ContainsKey(a[i] + 1))
            {
                dic.Add(a[i] + 1, 1);
            }
            else
            {
                dic[a[i] + 1]++;
            }

            if (!dic.ContainsKey(a[i] - 1))
            {
                dic.Add(a[i] - 1, 1);
            }
            else
            {
                dic[a[i] - 1]++;
            }
        }

        long ans = 0;
        ans = dic.Values.Max();
        Console.WriteLine(ans);
    }
}