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: Time Limit Exceeded)

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

namespace ConsoleApp103 {
    class Program {
        static void Main(string[] args) {
            int N = int.Parse(Console.ReadLine());

            var a = Console.ReadLine().Split().Select(int.Parse).ToArray();

            Array.Sort(a);

            //候補は(a[0] + 1) ~ (a[N - 1] - 1)の間にある
            int ans = a.Where(x => (x >= a[0] && x <= a[0] + 2)).ToArray().Count();
            int kari = 0;

            //それぞれの数を数えておく
            var counter = new int[a[N -  1] + 3];
            for (int i = 0; i < N; i++) {
                counter[a[i]] = a.Where(x => x == a[i]).ToArray().Count();
            }

            for (int i = a[0] + 1; i <= a[N - 1] - 1; i++) {
                ans = Math.Max(counter[i - 1] + counter[i] + counter[i + 1], ans);
            }

            Console.WriteLine(ans);
        }
    }
}