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 System.IO;
using System.Text;

namespace AtCoderSolve
{
    class Solve
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            int N = int.Parse(Console.ReadLine());
            var a = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int[] cnt = new int[100007];
            for(var i = 0; i < 100007; i++)
            {
                cnt[i] = 0;
            }

            for(var i = 0; i < N; i++)
            {
                if (a[i] > 0) { cnt[a[i] - 1]++; }
                cnt[a[i]]++;
                cnt[a[i] + 1]++;
            }
            Console.WriteLine(cnt.Max());

            Console.Out.Flush();
        }
    }
}