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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            Scanner cin = new Scanner();
            int N = cin.Int();
            int[] A = cin.ArrayInt(N);

            var a = A.Distinct().ToArray();
            int ans = 0, tmp = 0;
            for (int j = 0; j < a.Length; j++)
            {
                tmp = 0;
                for(int i = 0; i < N; i++)
                {
                    if (a[j] - 1 <= A[i] && A[i] <= a[j] + 1) tmp++;
                }
                ans = Math.Max(ans, tmp);
            }

            Console.WriteLine(ans);
            Console.ReadLine();
        }

        static int BinarySearch<T>(T[] array, T target) where T : IComparable<T> //2分探索
        {
            int min = 0;
            int max = array.Length - 1;

            while (true)
            {
                // 範囲内に見つからなかった
                if (max < min) return -1;
                // 範囲内の中央値と比較する
                int mid = min + (max - min) / 2;
                switch (target.CompareTo(array[mid]))
                {
                    case -1:    // 中央値より小さい
                        max = mid - 1;
                        break;
                    case 1:     // 中央値より大きい
                        min = mid + 1;
                        break;
                    case 0:     // 見つかった
                        return mid;
                }
            }
        }

        static void Swap<T>(ref T a, ref T b)
        {
            T tmp = a;
            a = b;
            b = tmp;
        }
    }

    class Scanner //標準入力
    {
        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 Int()
        {
            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] = Int() + add;
            }
            return Array;
        }

        public long Long()
        {
            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] = Long() + add;
            }
            return Array;
        }

        public double Double()
        {
            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] = Double() + add;
            }
            return Array;
        }
    }
}