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;
use std::io::{BufRead, Write};

fn solve<R: BufRead, W: Write>(mut input: R, mut output: W) {
    let mut buf = String::new();
    input.read_line(&mut buf).unwrap();
    let _n: usize = buf.trim_right().parse().unwrap();
    buf.clear();
    input.read_line(&mut buf).unwrap();
    let x: Vec<usize> = buf.split_whitespace().map(|s| s.parse().unwrap()).collect();
    let mut sorted = x.clone();
    sorted.sort();
    let half = x.len() / 2;
    for item in &x {
        let idx = sorted.binary_search(item).unwrap();
        writeln!(
            output,
            "{}",
            if idx < half {
                sorted[half]
            } else {
                sorted[half - 1]
            }
        ).unwrap();
    }
}

fn main() {
    let stdin = io::stdin();
    let stdout = io::stdout();
    solve(stdin.lock(), stdout.lock());
}

#[cfg(test)]
mod tests {
    fn test(input: &str, output: &str) {
        let mut v: Vec<u8> = Vec::new();
        ::solve(input.as_bytes(), &mut v);
        assert_eq!(String::from_utf8(v).unwrap(), output);
    }

    #[test]
    fn case1() {
        test(
            "4
2 4 4 3
",
            "4
3
3
4
",
        );
    }

    #[test]
    fn case2() {
        test(
            "2
1 2
", "2
1
",
        );
    }

    #[test]
    fn case3() {
        test(
            "6
5 5 4 4 3 3
", "4
4
4
4
4
4
",
        );
    }
}