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 Ruby (2.3.3) (judge verdict: Wrong Answer)

n = gets.chomp.to_i
arr = gets.chomp.split(' ').map(&:to_i)

sorted_arr = arr.dup
sorted_arr.sort!

def comb_case(max, min)
  case_num = 1
  (1..min).each do |i|
    case_num *= (max - i + 1)
  end
  (1..min).each do |i|
    case_num /= i
  end
  return case_num
end


def binary_search(arr, n, key)
  left = 0
  right = n
  while left < right
    mid = (left + right) / 2
    if arr[mid] == key
      return mid
    elsif key < arr[mid]
      right = mid
    else
      left = mid + 1
    end
  end
  return left
end

max_case = 0
max_comb = []

sorted_arr.each_with_index do |item, index|
  key = (item + 1) / 2
  cand_max = binary_search(sorted_arr, n, key)
  cand_min = cand_max - 1

  case_max = comb_case(item, sorted_arr[cand_max])
  if case_max > max_case
    max_case = case_max
    max_comb = [item, sorted_arr[cand_max]]
  end

  case_min = comb_case(item, sorted_arr[cand_min])
  if case_min > max_case
    max_case = case_min
    max_comb = [item, sorted_arr[cand_min]]
  end
end

puts max_comb.join(' ')