Problem:
Score : 400 points

Problem Statement

Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order.
From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized.
If there are multiple pairs that maximize the value, any of them is accepted.

Constraints

2 \leq n \leq 10^5

0 \leq a_i \leq 10^9

a_1,a_2,...,a_n are pairwise distinct.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

n
a_1 a_2 ... a_n

Output

Print a_i and a_j that you selected, with a space in between.

Sample Input 1

5
6 9 4 2 11

Sample Output 1

11 6

\rm{comb}(a_i,a_j) for each possible selection is as follows:

\rm{comb}(4,2)=6

\rm{comb}(6,2)=15

\rm{comb}(6,4)=15

\rm{comb}(9,2)=36

\rm{comb}(9,4)=126

\rm{comb}(9,6)=84

\rm{comb}(11,2)=55

\rm{comb}(11,4)=330

\rm{comb}(11,6)=462

\rm{comb}(11,9)=55

Thus, we should print 11 and 6.

Sample Input 2

2
100 0

Sample Output 2

100 0

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

#include <bits/stdc++.h>
#define int long long
using namespace std;

signed main() {
  int N;
  int ansx,x,a,b,c;
  ansx=0;x=1;
  cin>>N;
  vector<int>v(N);
  for(int i=0;i<N;i++)cin>>v[i];
  sort(v.begin(),v.end());
  for(int i=0;i<N-1;i++){
    for(int j=i+1;j<N;j++){
      if(v[i]*2<v[j])c=v[i];
      else c=v[j]-v[i];
      for(int k=0;k<c;k++){
        x=x*(v[j]-k)/(k+1);
      }
      if(ansx<x){a=v[i];b=v[j];ansx=x;}
      x=1;
    }
  }
  cout<<b<<" "<<a<<endl;
}