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.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;
using static kyoupuro.Input;
using static kyoupuro.MyMath;

namespace kyoupuro {

    class MainClass {

        public static void Main() {
            var N = NextInt();
            var list = IntList();
            list.Sort();

            var first = 0;
            var last = list.FindIndex(x => x != list[0]);
            last = last == -1 ? N : last;
            var result = last - first;

            for (int now = 0; now <= 100000 && last < N; now++) {
                while (first < N && list[first] < now - 1) first++;
                while (last < N && list[last] < now + 2) last++;

                result = Math.Max(result, last - first);
            }

            Console.WriteLine(result);

            //Console.WriteLine(Enumerable.Range(0, 100001).Max(x => list.Count(y => y - 1 <= x && x <= y + 1)));
        }
    }

    class MyMath {
        static long Gcd(long a, long b) {
            return b == 0 ? a : Gcd(b, a % b);
        }
    }

    class Input {
        static IEnumerator<string> enumerator = new string[] { }.AsEnumerable().GetEnumerator();

        public static string Line() {
            return Console.ReadLine();
        }

        public static int NextInt() {
            while (!enumerator.MoveNext()) {
                enumerator = StrArr().AsEnumerable().GetEnumerator();
            }
            return int.Parse(enumerator.Current);
        }

        public static long NextLong() {
            while (!enumerator.MoveNext()) {
                enumerator = StrArr().AsEnumerable().GetEnumerator();
            }
            return long.Parse(enumerator.Current);
        }

        public static string[] StrArr() {
            return Line().Split(' ');
        }

        public static List<int> IntList() {
            return StrArr().Select(int.Parse).ToList();
        }

        public static List<long> LongList() {
            return StrArr().Select(long.Parse).ToList();
        }

        public static void Skip(int line = 1) {
            enumerator.Reset();
            for (int i = 0; i < line; i++) Console.ReadLine();
        }

        public static void Reset() {
            enumerator.Reset();
        }
    }
}