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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        for(int i = 0;i < n;i++) a[i] = sc.nextInt();

        Arrays.sort(a);
        for(int i = 0;i < a.length / 2;i++) {
            int tmp = a[i];
            a[i] = a[a.length - 1 - i];
            a[a.length - 1 - i] = tmp;
        }
        
        if(a.length == 2) {
            System.out.println(a[0] + " " + a[1]);
        }
        else {
            long max = -1;
            long maxN = -1;
            long maxR = -1;
            for(int i = 0;i < a.length;i++) {
                int candidate1 = a[(a.length - i) / 2];
                int candidate2 = a[1 + ((a.length - i) / 2)];
                
                long num = nCr(a[i], candidate1);
                long num2 = nCr(a[i], candidate2);
                long big = num > num2 ? num : num2;
                
                if(max < big) {
                    max = big;
                    maxN = a[i];
                    if(num > num2) maxR = candidate1;
                    else maxR = candidate2;
                }
            }

            System.out.println(maxN + " " + maxR);
        }
    }
    
    private static long nCr(long n, long k) {
        long r = 1;
        for(long d = 1;d <= k;d++) {
            r *= n--;
            r /= d;
        }
        return r;
    }
    
}