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-mcs 6.8.0.105) (judge verdict: Runtime Error)

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

namespace AtCoder.Abc
{
    public class ABC072C
    {
        public static void Main(string[] args)
        {
            // 整数の入力
            long n = long.Parse(Console.ReadLine());

            // 整数配列の入力
            var inputLongArray = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();

            var duplicationList = inputLongArray
                .GroupBy(i => i)
                .Where(g => g.Count() > 1)
                .Max();

            if (duplicationList == null) {
                if (n >= 3) {
                    Console.WriteLine(3);
                } else {
                    Console.WriteLine(n);
                }
                return;
            }
            var distinctMaxCount = duplicationList.Count();

            var zengo = inputLongArray.Where(x => x == duplicationList.Key + 1 || x == duplicationList.Key - 1).Count();
            var mae = inputLongArray.Where(x => x == duplicationList.Key - 1 || x == duplicationList.Key - 2).Count();
            var next = inputLongArray.Where(x => x == duplicationList.Key + 1 || x == duplicationList.Key + 2).Count();

            var result = Math.Max(Math.Max(zengo, mae), next);

            Console.WriteLine(distinctMaxCount + result);

        }

    }
}