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

class Program {
    internal static void Main(string[] args) {
        int N = int.Parse(ReadLine());
        var a = ReadLine().Split(' ').Select(s => int.Parse(s)).ToList();
        var dic = new Dictionary<int, int>();

        for (int i = 0; i < N; i++) {
            if (dic.ContainsKey(a[i])) {
                dic[a[i]]++;
            } else {
                dic.Add(a[i], 1);
            }
        }

        var cnt = 0;
        int take = 3;
        int loop = N - 2;
        if (N < 3) {
            take = N;
            loop = N;
        }
        for (int i = 0; i < loop; i++) {
            var tmp = dic.Select(kvp => kvp.Value).Skip(i).Take(take).Sum();
            cnt = Math.Max(tmp, cnt);
        }

        WriteLine(cnt);
    }
}