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 Common Lisp (SBCL 1.1.14) (judge verdict: Time Limit Exceeded)

(defun fact (n)
  (labels ((rec (n a) (if (= n 0) a (rec (1- n) (* n a)))))
    (rec n 1)))

(defmacro comb (n r) `(/ (fact ,n) (* (fact ,r) (fact (- ,n ,r))))) ;; nCr

(defun solver ()
  (let* ((n (read)) (ai (make-array n :fill-pointer 0))
         sorted-ai m (max 0) (cmax1 0) (cmax2 0) temp answer (pre -1))
    (loop repeat n do
          (vector-push (read) ai))
    (setf sorted-ai (sort (copy-seq ai) #'>))
    (setf max (aref sorted-ai 0))
    (setf m (floor (/ n 2)))
    (loop for i from m below n do
          (setf temp (comb max (aref sorted-ai i)))
          (when (< temp pre) (break))
          (when (> temp cmax1)
            (setf cmax1 temp) (setf answer (aref sorted-ai i))))
    (loop for i from m downto 0 do
          (setf temp (comb max (aref sorted-ai i)))
          (when (< temp pre) (break))
          (when (> temp cmax2)
            (setf cmax2 temp) (setf answer (aref sorted-ai i))))
    (format t "~a ~a~%" max answer)))

(solver)