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: Runtime Error)

(defun input (n)
  (let ((a (make-array n)))
    (loop for i below n do (setf (aref a i) (read)))
    a))

(defparameter p (make-array 15000 :element-type 'integer :initial-element 0))
(setf (aref p 0) 1)
(setf (aref p 1) 1)
(defun fact (n)
  (if (< 0 (aref p n))
    (aref p n)
    (progn (setf (aref p n) (* n (fact (1- n))))
           (aref p n))))

(defun solve (n A)
  (let ((ans nil)
        (f 0))
    (loop for i from 1 below n
          do (loop for j below i 
                   for ai = (aref A i) for aj = (aref A j)
                   for x = (/ (fact ai) (fact aj) (fact (- ai aj)))
                   when (> x f)
                   do (progn (setq ans (cons (aref a i) (aref a j)))
                             (setq f x))))
    ans))

(let* ((n (read))
      (a (sort (input n) #'<))
      (e (solve n a)))
  (format t "~A ~A~%" (car e) (cdr e)))