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: Time Limit Exceeded)

using System;
using System.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace ABC_practice
{
    public class Program
    {

        #region templete

        private static void WL(string s) { WriteLine(s); }

        /// <summary>
        /// 最小公倍数
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <returns></returns>
        static long Gcd(long a, long b)
        {
            var v = new[] { a, b };
            while (v[1] != 0) { v = new[] { v[1], v[0] % v[1] }; }
            return v[0];
        }
        /// <summary>
        /// 最小公約数
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <returns></returns>
        static long Lcm(long a, long b) { return a / Gcd(a, b) * b; }

        static void chmax<T>(ref T a, T b) where T : IComparable<T> { a = a.CompareTo(b) < 0 ? b : a; }
        static void chmin<T>(ref T a, T b) where T : IComparable<T> { a = a.CompareTo(b) < 0 ? a : b; }

        public static void Main(string[] args)
        {
            new Program().Solve();
            ReadLine();
        }

        #endregion

        static Dictionary<int, int> dic;
        static int n;
        static int[] a;
        public void Solve()
        {
            var cin = new Scanner();
            n = cin.nextInt();
            a = new int[n];
            a = cin.ArrayInt(n);

            dic = new Dictionary<int, int>();

            for (int i = 0; i < n; i++)
            {
                proc(i);
            }
            WL($"{dic.Values.Max()}");

        }
        public static void proc(int index)
        {
            for (int ai = a[index]-1; ai <= a[index]+1; ai++)
            {
                if (!dic.ContainsKey(ai))
                {
                    var cnt = 0;
                    for (int j = 0; j < n; j++)
                    {
                        if (Inside(ai, a[j] - 1, a[j] + 1)) cnt++;
                    }
                    dic.Add(ai, cnt);
                }
            }
        }

        public static bool Inside(int x,int a,int b) { return (a <= x && x <= b) ? true : false; }

    }
}


#region console in

class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return next();
        i = 0;
        return s[i++];
    }

    public int nextInt()
    {
        return int.Parse(next());
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextInt() + add;
        }
        return Array;
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextLong() + add;
        }
        return Array;
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextDouble() + add;
        }
        return Array;
    }
}

#endregion