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 Lua (5.3.2) (judge verdict: Time Limit Exceeded)

local N=io.read("n")
local a={}
for i=1,N do
  a[i]=io.read("n")
end
function c(n,m)
  local res=0
  local s=1
  local k=1
  for i=n,n-m+1,-1 do
    s=s*i
  end
  for i=1,m do
    k=k*i
  end
  return s//k
end
table.sort(a,function (a,b) return a>b end)
local first=a[1]
local second=a[2]
local total=c(a[1],a[2])
for i=1,N-1 do
  for j=i+1,N do
    if c(a[i],a[j])>total then
      total=c(a[i],a[j])
      first=a[i]
      second=a[j]
    end
  end
end
print(first,second)