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) {

//        long startTime = System.currentTimeMillis();

        Scanner scanner = new Scanner(System.in);

        int N = scanner.nextInt();

        Long[] X = new Long[N];
        for (int i = 0; i < N; i++) {
            X[i] = scanner.nextLong();
        }
        scanner.close();

        Arrays.sort(X);

        Long[] ans = new Long[2];
        Long max = 0L;
        for (int i = 0; i < N; i++) {

            Long n = X[i];
            for (int j = 0; j < i; j++) {
                Long r = X[j];
                Long c = comb(n, r);
                if (c > max) {
                    ans[0] = n;
                    ans[1] = r;
                    max = c;
                }
            }
        }
        System.out.println(ans[0] + " " + ans[1]);
//        System.out.println(System.currentTimeMillis() - startTime);
    }

    private static long comb(Long n, Long r) {
        if (n < 0 || r < 0 || n < r) {
            throw new ArithmeticException("n = " + n + ", r = " + r);
        }
        r = Math.min(r, n - r); // nCr = nCn-r
        if (r == 1) {
            return n;
        }
        long sum = 1;
        for (int i = 1; i <= r; i++) {
            sum = sum * (n - i + 1) / i;
        }
        return sum;
    }
}