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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
#include <stdio.h>
#include <algorithm>
#include <map>
using namespace std;
#define r(i,n) for(int i=0;i<n;i++)
#define ll long long
#define rn(i,n) for(int i=1;i<=n;i++)

int main (){
  int n;
  cin>>n;
  vector<int> a(n);
  vector<int> s;
  int tmp;

  r(i,n){
    cin>>a.at(i);
    if(a.at(i)==0){
      s.push_back(a.at(i)+1);
      s.push_back(a.at(i));
    }else{
    s.push_back(a.at(i)+1);
    s.push_back(a.at(i));
    s.push_back(a.at(i)-1);
  }
  }
  //cout<<"hi"<<endl;
  unique(s.begin(),s.end());
  //cout<<s.size()<<endl;
  ll maxi=0;
  r(i,s.size()){
    ll cnt=0;
    //cout<<"hi"<<endl;
    r(j,n){
      if(s[i]==a.at(j))cnt++;
      else if(s[i]-1==a.at(j))cnt++;
      else if(s[i]+1==a.at(j))cnt++;
    }
    maxi=max(maxi,cnt);
  }

  cout<<maxi<<endl;

  return 0;
}