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;
using System.Collections.Generic;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var a = Console.ReadLine().Split().Select(int.Parse).ToArray();
            var dict = new Dictionary<int, int>();

            for (var i = 0; i < N; i++)
            {
                if (dict.ContainsKey(a[i]))
                    dict[a[i]]++;
                else
                    dict[a[i]] = 1;
            }

            var one = new KeyValuePair<int, int>(0, 0);
            var two = new KeyValuePair<int, int>(0, 0);
            var three = new KeyValuePair<int, int>(0, 0);
            int count = 0, max = 1;
            foreach (var d in dict.OrderBy(z => z.Key))
            {
                if (count == 0)
                    one = d;
                else if (count == 1)
                    two = d;

                if (N == 1) break;
                if (dict.Count == 2 && count == 1)
                {
                    if (one.Key + 1 == two.Key || one.Key + 2 == two.Key)
                        max = one.Value + two.Value;
                    break;
                }

                max = Math.Max(max, d.Value);
                if (count >= 2)
                {
                    three = d;
                    if (one.Key + 1 == two.Key)
                        max = Math.Max(max, one.Value + two.Value);
                    if (one.Key + 1 == two.Key && two.Key + 1 == three.Key)
                        max = Math.Max(max, one.Value + two.Value + three.Value);
                    if (one.Key + 2 == two.Key)
                        max = Math.Max(max, one.Value + two.Value);

                    one = two;
                    two = three;
                }
                count++;
            }

            Console.WriteLine(max);
        }
    }
}