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: Runtime Error)

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);

            var a_distinct = a.Distinct().ToArray();

            //それぞれの数を数えておく
            var counter = new int[a.Max() + 2];
            for (int i = 0; i < a_distinct.Count(); i++) {
                counter[a_distinct[i]] = a.Where(x => x == a_distinct[i]).ToArray().Count();
            }

            //候補は(a[0] + 1) ~ (a[N - 1] - 1)の間にある
            int ans = counter[a[0]] + counter[a[0] + 1] + counter[a[0] + 2];

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

            Console.WriteLine(ans);
        }
    }
}