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 Python (3.8.2) (judge verdict: Wrong Answer)

n = int(input())
a = list(map(int, input().split()))

# nCrにおいてrが一定の時にnが最大の時に場合の数が最大になる
# max_xCrとnCmax_xを全て調べればO(N)

def calc_comb(n, r):
    x = 1
    y = 1
    lc = r
    for _ in range(lc):
        x *= n 
        y *= r
        n -= 1
        r -= 1
    return x//y

max_a = max(a)
res = [calc_comb(max_a, x) if x != max_a else -1 for x in a] 
import numpy as np
idx = np.argmax(res) % len(a)
print(res)
print('{:d} {:d}'.format(max_a, a[idx]))