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.Linq;

namespace ABC072Cother
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int[] a = Console.ReadLine().Split(' ').Select(temp => int.Parse(temp)).ToArray();

            int[] all = new int[3 * n];
            for (int i = 0; i < n; i++)
            {
                all[i] = a[i];
                all[i + n] = a[i] - 1;
                all[i + n + n] = a[i] + 1;
            }

            Array.Sort(all);
            int before = -1111;
            int cur = 1;
            int max = 1;
            for (int i = 0; i < n * 3; i++)
            {
                if (all[i] == before)
                {
                    cur++;
                }
                else
                {
                    cur = 1;
                }

                before = all[i];
                if (cur > max)
                {
                    max = cur;
                }
            }
            Console.WriteLine(max);
        }
    }
}