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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Control.Applicative
import Control.Monad
import Data.List
import Data.Maybe


main :: IO()
main = do
    _ <- getLine
    nums <- map read . words <$> getLine
    putStrLn $ solve nums

solve :: [Integer] -> String
solve nums =
    case maxCombPair of
        (_, (a1', a2')) -> show a1' ++ " " ++ show a2'
    where
        pairs = [(a1, a2) | a1 <- nums, a2 <- nums, a1 > a2]
        maxCombPair = foldl (\temp pair -> if (fromJust $ comb pair) > fst temp then (fromJust $ comb pair, pair) else temp) (0, (0, 0)) pairs

comb :: (Integer, Integer) -> Maybe Integer
comb (a1, a2)
    | a1 <= a2 = Nothing
    | a2 == 0 = Just 1
    | a1 - a2 < a2 = comb (a1, a1 - a2)
    | otherwise = Just $ (foldl1 (*) . take (fromIntegral a2) $ reverse [0..a1]) `div` (foldl1 (*) [1..a2])