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 ABC072C
{
    class Program
    {
        static void Main(string[] args)
        {
            new Solver().Solve();
        }
    }

    class Solver
    {
        int N;
        int[] a;

        public void Solve()
        {
            // S[x] : ai = x となるaiの数
            Dictionary<int, int> S = new Dictionary<int, int>();

            // S をセット
            foreach (int ai in a) {
                if (S.ContainsKey(ai)) {
                    S[ai]++;
                }
                else {
                    S[ai] = 1;
                }
            }

            // 拡大定義域
            HashSet<int> DIx = new HashSet<int>();

            foreach (var expandedKey in S.Keys.Select(x => new Tuple<int, int, int>(x - 1, x, x + 1))) {
                DIx.Add(expandedKey.Item1);
                DIx.Add(expandedKey.Item2);
                DIx.Add(expandedKey.Item3);
            }

            // I[x] : 操作後のai = x となりうるiの数
            Dictionary<int, int> I = new Dictionary<int, int>();

            // I[x] = S[x-1] + S[x] + S[x+1]
            foreach (int x in DIx) {
                int value;
                S.TryGetValue(x - 1, out value);
                I[x] = value;
                S.TryGetValue(x, out value);
                I[x] += value;
                S.TryGetValue(x + 1, out value);
                I[x] += value;
            }

            int ans = I.Values.Max();
            Console.WriteLine(ans);
        }

        public Solver()
        {
            N = ReadInt();
            a = ReadIntArray();
        }

        static String ReadString() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Console.ReadLine()); }
        static long ReadLong() { return long.Parse(Console.ReadLine()); }
        static double ReadDouble() { return double.Parse(Console.ReadLine()); }
        static String[] ReadStringArray() { return Console.ReadLine().Split(' '); }
        static int[] ReadIntArray() { return Console.ReadLine().Split(' ').Select(e => int.Parse(e)).ToArray(); }
        static long[] ReadLongArray() { return Console.ReadLine().Split(' ').Select(e => long.Parse(e)).ToArray(); }
        static double[] ReadDoubleArray() { return Console.ReadLine().Split(' ').Select(e => double.Parse(e)).ToArray(); }
    }

}