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 <iostream>
#include <vector>
#include <algorithm>

using namespace std;


double comb(int x, int y){
    double r = 1;
    double n = 1;
    double n_r = 1;
    
    for(int i = x - y + 1; i <= x; i++){
        n *= i;
    }
    for(int i = 1; i <= y; i++){
        r *= i;
    }
    return n / (r * n_r);
}

int main(void){

    int N;
    vector<int> X, tempX;
    cin >> N;
    
    int temp;
    
    for(int i = 0; i < N; i++){
        cin >> temp;
        X.push_back(temp);
        tempX.push_back(temp);
    }
    
    sort(X.rbegin(), X.rend());
    int max_i, max_j;
    double max = 0;
    for(int i = 0; i < N - 1; i++){
        for(int j = i + 1; j < N; j++){
            double temp = comb(X[i], X[j]);
            if(temp > max){
                max_i = X[i];
                max_j = X[j];
                max = temp;
            }
        }
    }
    cout << max_i << " " << max_j << endl;
}