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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"fmt"
	"sort"
)

func main() {
	var N int
	fmt.Scan(&N)
	A := make([]int, N)
	for i := 0; i < N; i++ {
		var V int
		fmt.Scan(&V)
		A[i] = V
	}
	sort.Ints(A)
	mid := float64(A[len(A)-1]) / 2
	x := lowerBound(A, mid)

	if A[len(A)-1] == A[x] {
		x -= 1
	}
	fmt.Println(A[len(A)-1], A[x])
}

func lowerBound(arr []int, target float64) int {
	l, r := -1, len(arr)+1
	for r > l {
		mid := (r + l) / 2
		if float64(arr[mid]) < target {
			l = mid + 1
		} else {
			r = mid
		}
	}
	return l
}