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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Math;

class Atcoder_nA{
  public static void Main(){

    int n = int.Parse(Console.ReadLine());
    int[] a = new int[n];
    int[] b = new int[100010];
    for (int i = 0; i < n; i++){
        a[i] = int.Parse(Console.ReadLine());
        b[a[i]]++;
    }

    int m = 0;
    int index = 0;
    for(int i=1; i<100010; i++){
      if(b[i-1] + b[i] + b[i+1] > m){
        m = b[i-1] + b[i] + b[i+1];
        index = i;
      }
    }

    Console.WriteLine(index);
  }
}