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;

namespace MyProgram{
    class AtCoder{
        static void Main(){
            int N = int.Parse(Console.ReadLine());
            int[] a = Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);
            int a_max = 0;
            for(var i=0;i<N;i++){
                a_max = Math.Max(a_max,a[i]);
            }
            int[] count = new int[a_max+1];
            for(var i=0;i<N;i++){
                count[a[i]]++;
            }
            int max_X = 0;
            for(var i=1;i<a_max;i++){
                int sum = count[i-1] + count[i] + count[i+1];
                max_X = Math.Max(sum,max_X);
            }
            max_X = Math.Max(count[0],max_X);
            max_X = Math.Max(count[a_max],max_X);
            Console.WriteLine(max_X);
        }
    } 
}