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;

class Dmondai
{
    static void Main()
    {
        var N = Int32.Parse(Console.ReadLine());
        var a = Console.ReadLine().Split(' ').Select(x => Int32.Parse(x)).OrderBy(x=>x).ToArray();
        var min = a[0]-1;
        var max=a[N - 1]+1;
        var list = new List<int[]>();
        var currentNum = a[0];
        var currentNumCount = 1;
        for (int i=1;i<N;++i)
        {

            if (currentNum != a[i])
            {
                list.Add(new int[] { currentNum, currentNumCount});
                currentNum = a[i];
                currentNumCount=1;
            }
            else currentNumCount++;
            if(i==N-1) list.Add(new int[] { currentNum, currentNumCount });
        }
        var count =0;
        var ans = int.MinValue;
        for (var x=min;x<=max;++x)
        {
            count = list.Where(num => num[0] == x || num[0] == x - 1 || num[0] == x + 1).Sum(num => num[1]);
            if (ans < count) ans = count;
        }
        Console.WriteLine(ans);
    }
}