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 (1.42.0) (judge verdict: Accepted)

use std::io::*;
use std::str::FromStr;
use std::cmp;
use std::collections::HashMap;
use std::collections::HashSet;
use std::char;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char) 
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn gcd(a: u64, b: u64) -> u64 {
    if b == 0 {
        a
    } else {
        gcd(b, a % b)
    }
}
fn read_tuple2<T: FromStr, S: FromStr>() -> (T, S) {
    let a = read();
    let b = read();
    (a, b)
}

fn count_two(n: u64) -> u64 {
    fn go(count:u64, num: u64) -> u64 {
        if num % 2 == 0 {
            go(count +1, num / 2)
        } else {
            count
        }
    }
    go(0, n)
}

fn main() {
    let n: usize = read();
    let xs: Vec<u64> = (0..n).map(|_|read()).collect();
    let mut xs_sorted: Vec<u64> = xs.clone();
    xs_sorted.sort();
    let middle = xs_sorted[n / 2];
    let middle_m1 = xs_sorted[n / 2 - 1];
    for x in xs {
        println!("{}", if x < middle { middle } else {middle_m1} );
    }
}