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 Rust (1.15.1) (judge verdict: Time Limit Exceeded)

#![allow(unused)]

#[allow(unused_imports)]
use std::{cmp, collections, fmt, io, iter, ops, str};
use cmp::Ordering::*;
use collections::{HashMap, HashSet};
use io::{Read, Write};

#[cfg(feature = "debug")]
macro_rules! debug {
    ($fmt: expr) => { eprintln!($fmt) };
    ($fmt: expr, $($arg: tt)*) => { eprintln!($fmt, $($arg)*) };
}

#[cfg(not(feature = "debug"))]
macro_rules! debug {
    ($fmt: expr) => {};
    ($fmt: expr, $($arg: tt)*) => {};
}

fn read_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.trim().to_owned()
}

fn read_word() -> String {
    const CAPACITY: usize = 16;

    let mut stdin = io::stdin();
    let mut byte: [u8; 1] = [0];

    loop {
        let mut buf = Vec::with_capacity(CAPACITY);

        loop {
            let res = stdin.read(&mut byte);

            if res.unwrap_or(0) == 0 || byte[0] <= b' ' {
                break;
            } else {
                buf.push(byte[0]);
            }
        }

        if buf.len() > 0 {
            return String::from_utf8(buf).unwrap();
        }
    }
}

fn parse_line<T: str::FromStr>() -> T {
    read_line().parse().ok().unwrap()
}

fn parse_word<T: str::FromStr>() -> T {
    read_word().parse().ok().unwrap()
}

fn parse_vec<T: str::FromStr>() -> Vec<T> {
    read_line()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn flush() {
    io::stdout().flush();
}

fn main() {
    let _ = parse_line::<usize>();
    let mut a = parse_vec::<i32>();

    a.sort_by(|x, y| y.cmp(x));

    let n = a[0];
    let mut comb = a[1..]
        .iter()
        .map(|x| (*x, combination(n, *x)))
        .collect::<Vec<_>>();
    comb.sort_by(|&(x, c), &(x2, c2)| c2.cmp(&c));

    println!("{} {}", n, comb[0].0);
}

fn combination(n: i32, k: i32) -> i32 {
    assert!(n >= k);

    let mut ans = 1;

    for i in 0..k {
        ans *= n - i;
    }
    for i in 1..(k + 1) {
        ans /= i;
    }

    ans
}