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::FromStr;
use std::cmp::{min, max};
use std::mem::swap;
use std::collections::HashMap;

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

static DX: &'static [i32] = &[0, 0, 1, -1];
static DY: &'static [i32] = &[1, -1, 0, 0];

fn main() {
    let n: usize = read();

    let mut x: Vec<[usize; 2]> = (0..n).map(|i| [i, read()]).collect();

    x.sort_by_key(|item| item[1]);

    let mut mid = n / 2;

    let mut ans = vec![0; n];

    for i in 0..n {
        if i == mid {
            mid -= 1;
        }

        ans[x[i][0]] = x[mid][1];
    }

    for i in 0..n {
        println!("{}", ans[i]);
    }
}

fn pow_mod(mut n: u64, mut exp: u64, m: u64) -> u64 {
    let mut t = 1;

    n %= m;

    while exp > 1 {
        if exp & 1 == 1 {
            t *= n;
            t %= m;
        }

        n *= n;
        n %= m;
        exp >>= 1;
    }

    (n * t) % m
}