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: Wrong Answer)

import java.util.*;


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();
        }
        long max = 0;
                    int ansA = 0;
            int ansB = 0;
        for(int i = 0; i < n; i++){
            int low = 0;
            int high = n - 1;
            int maxMid = 0;
            int temp = 100000;
            int target = (a[i] + 1) / 2;
            int mid = 0;
            while(low <= high){
                mid = (low + high) / 2;
                if(a[mid] == target){
                    maxMid = a[mid];
                } else if(Math.abs(target - a[mid]) < temp) {
                    temp = a[mid];
                }
                if(a[mid] > target){
                    low = mid + 1;
                } else{
                    high = mid - 1;
                }
            }
                if(maxMid == 0){
                    temp = maxMid;
                }
                long x = calc(a[i], maxMid);
                if(x > max){
                    max = x;
                    ansA = a[i];
                    ansB = a[mid];
                }
        }
        System.out.print(ansA);
        System.out.print(" ");
        System.out.print(ansB);
    }
    static long calc(int n, int m){
            long c = 1;
    m = ( n - m < m ? n - m : m );
    for( int ns = n - m + 1, ms = 1; ms <= m; ns ++, ms ++ ) {
        c *= ns;
        c /= ms;
    }
    return c;
    }
}