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::str::*;

fn read<T: FromStr>() -> Option<T> {
    let stdin = stdin();
    let s = stdin
        .bytes()
        .map(|c| c.unwrap() as char)
        .take_while(|c| !c.is_whitespace())
        .collect::<String>();
    s.parse::<T>().ok()
}

fn read_nums(limit_num: usize) -> Vec<i32> {
    let mut vec: Vec<i32> = Vec::new();
    while let Some(n) = read() {
        vec.push(n);
        if vec.len() == limit_num {
            break;
        }
    }
    return vec;
}

fn main() {
    let n: usize = read().unwrap();
    let x_list = read_nums(n);
    let mut sorted = x_list.clone();
    sorted.sort_by(|a, b| a.cmp(b));
    let half = (n as f32 / 2.0).floor() as usize;
    for i in 0..n {
        if sorted.binary_search(&x_list[i]).unwrap() <= half - 1 {
            println!("{}", sorted[half]);
        } else {
            println!("{}", sorted[half - 1]);
        }
    }
}