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.Text;
using System.Threading.Tasks;
using static System.Console;
namespace AtCoder.ARC082
{
    class Together
    {
        public static void Main()
        {
            var n = int.Parse(ReadLine());
            var nums = new int[100001].ToArray();
            foreach(var a in ReadLine().Trim().Split(' ').Select(_ => int.Parse(_))) {
                nums[a + 1]++;
            }
            var max = 0;
            for(var i = 1; i < nums.Length - 1; ++i) {
                if (nums[i - 1] + nums[i] + nums[i + 1] > max) {
                    max = nums[i - 1] + nums[i] + nums[i + 1];
                }
            }
            WriteLine(max);
        }
    }

}