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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

# https://atcoder.jp/contests/abc094/tasks/arc095_b
n = int(input())
nums = [int(i) for i in input().split()]

# すべてを計算する時間はなさそう
# 最大のモノを選らんで、それと絶対値差が大きいモノを選ぶ。いや、ここは全部やればいいのかな。
mod = (10 ** 9 + 7) ** 2
MAX = 2 * (10 ** 6) + 1 # これは変動するので注意。せいぜい10 ** 6くらいまでがTLEの限界

def com_init(MAX, mod):
    fac = [0] * MAX
    finv = [0] * MAX
    inv = [0] * MAX
    fac[0] = fac[1] = 1
    finv[0] = finv[1] = 1
    inv[1] = 1
    for i in range(2, MAX):
        fac[i] = fac[i - 1] * i % mod
        inv[i] = mod - inv[mod % i] * (mod // i) % mod
        finv[i] = finv[i - 1] * inv[i] % mod
    return fac, finv

fac, finv = com_init(MAX, mod)

def nCr(n, r):
    if n < r:
        return 0
    elif n < 0 or r < 0:
        return 0
    return fac[n] * (finv[r] * finv[n - r] % mod) % mod

t = -float('inf')
MAX = max(nums)
ans = None
for num in nums:
    if num == MAX:
        continue
    r = nCr(MAX, num)
    if r > t:
        t = r
        ans = (MAX, num)
print(*ans)