Problem:
Score : 300 points

Problem Statement

When l is an odd number, the median of l numbers a_1, a_2, ..., a_l is the (\frac{l+1}{2})-th largest value among a_1, a_2, ..., a_l.

You are given N numbers X_1, X_2, ..., X_N, where N is an even number.
For each i = 1, 2, ..., N, let the median of X_1, X_2, ..., X_N excluding X_i, that is, the median of X_1, X_2, ..., X_{i-1}, X_{i+1}, ..., X_N be B_i.

Find B_i for each i = 1, 2, ..., N.

Constraints

2 \leq N \leq 200000

N is even.

1 \leq X_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
X_1 X_2 ... X_N

Output

Print N lines.
The i-th line should contain B_i.

Sample Input 1

4
2 4 4 3

Sample Output 1

4
3
3
4

Since the median of X_2, X_3, X_4 is 4, B_1 = 4.

Since the median of X_1, X_3, X_4 is 3, B_2 = 3.

Since the median of X_1, X_2, X_4 is 3, B_3 = 3.

Since the median of X_1, X_2, X_3 is 4, B_4 = 4.

Sample Input 2

2
1 2

Sample Output 2

2
1

Sample Input 3

6
5 5 4 4 3 3

Sample Output 3

4
4
4
4
4
4

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::io::{stdout, BufWriter, Write};
use std::thread;

fn run() {
    let input = read_input();
    let mut input = input.split_whitespace();
    let in_n: i64 = input.next().unwrap().parse().unwrap();
    let in_x: Vec<i64> = input.map(|s| s.parse().unwrap()).collect();

    let mut y = in_x.clone();
    y.sort();
    let x1 = y[in_n as usize / 2 - 1];
    let x2 = y[in_n as usize / 2];

    let out = stdout();
    let mut out = BufWriter::new(out.lock());
    for x in in_x {
        writeln!(out, "{}", if x <= x1 { x2 } else { x1 }).unwrap();
    }
}

fn main() {
    thread::Builder::new()
        .stack_size(32 * 1024 * 1024) // 32MB
        .spawn(run)
        .unwrap()
        .join()
        .unwrap();
}

/// ローカル環境なら _in.txt から入力を受ける
fn read_input() -> String {
    use std::fs::File;
    use std::io::Read;
    let mut s = String::new();
    match option_env!("LOCAL") {
        Some(_) => File::open("src/_in.txt")
            .expect("File not found")
            .read_to_string(&mut s)
            .unwrap(),
        None => std::io::stdin().read_to_string(&mut s).unwrap(),
    };
    s
}