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 (3.4.3) (judge verdict: Time Limit Exceeded)

import sys
from functools import reduce


def input():
    return sys.stdin.readline().strip()


sys.setrecursionlimit(10 ** 9)

MOD = 10 ** 9 + 7


def main():
    def cmb(N, A):
        num = reduce(lambda x, y: x * y % MOD, range(N, N - A, -1))
        den = reduce(lambda x, y: x * y % MOD, range(1, A + 1))
        # pow(den,MOD-2,MOD)はdenの逆元
        return num * pow(den, MOD - 2, MOD) % MOD

    N = int(input())
    A = list(map(int, input().split()))
    A.sort()
    n = A[-1]
    C = 0
    ans = -1
    for a in A:
        if a == 0:
            c = 1
        else:
            c = cmb(n, a)
        if c > C:
            C = c
            ans = a
        elif c < ans:
            break

    print(n, ans)


if __name__ == "__main__":
    main()