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: Runtime Error)

import java.math.BigInteger;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int N = scan.nextInt();
        int[] data = new int[N];
        for(int i = 0; i < N; i++) {
            data[i] = scan.nextInt();
        }
        Arrays.sort(data);
        int max = data[N-1];
        BigInteger[] big = new BigInteger[max+1];
        Arrays.fill(big, BigInteger.ONE);
        for(int i = 1; i <= max; i++) {
            big[i] = big[i-1].multiply(new BigInteger(Integer.toString(i)));
        }
        BigInteger answer = BigInteger.ZERO;
        int m = 0;
        int n = 0;
        for (int i = data.length - 1; 0 <= i; i--) {
            for (int j = 0; j < i; j++) {
                BigInteger target = big[data[i]].divide(big[data[j]]).divide(big[data[i]-data[j]]);
                if (answer.compareTo(target) < 0) {
                    m = i;
                    n = j;
                    answer = target;
                } else {
                    continue;
                }
            }
        }
        System.out.printf("%d %d\n", data[m], data[n]);
    }
}