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 (2.7.1) (judge verdict: Runtime Error)

#これがコンビネーションの定義だよ
def C(n,k)
  if n==1
    return 1
  elsif k==0 || k==n
    return 1
  else
    return C(n-1,k-1)+C(n-1,k)
  end
end

n = gets.to_i
num = gets.strip.split.map(&:to_i)
num.sort!
#パスカルの三角形を考えればnとして選ぶのはnumの最大値
maxs = num.max
ary = Array.new(n-1,0)
#全探索してもO(N)
i = 0
while i < n-1
  ary[i] = C(maxs,num[i])
  i += 1
end
puts [maxs,num[ary.index(ary.max)]].join(" ")