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: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
using System.Linq;
using E = System.Linq.Enumerable;
 
class Program
 {

        static void Main(string[] args)
        {
          //入力を受け取る
          var N = long.Parse(Console.ReadLine());
          var A = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
          var youso = A.Max();
          var ans = new long[youso+1];
          
          for(long i = 0; i < N ; i++){
            var num = A[i];
            ans[num]++;
          }
          
          var B = new long[youso];
          for(long i = 0; i < B.Length ; i++){
            B[i] = 0;
          }
          var max = 0L;
          for(long i = 1; i < youso;i++){
            B[i] = ans[i-1]+ans[i]+ans[i+1];
            if(B[i] > max){
              max = B[i];
            }
          }
          Console.WriteLine(max);
        }
  
}