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: Time Limit Exceeded)

#![allow(unused_imports)]
use proconio::{input, fastout};
use proconio::marker::*;
use std::cmp::Ordering;
use std::collections::HashMap;

#[fastout]
fn main() {
  input! {
    n: usize,
    vals: [usize;n]
  }

  let mut vis = vals
  .into_iter()
  .enumerate()
  .map(|(i, v)| (i, v))
  .collect::<Vec<(usize, usize)>>();
  vis.sort_by(|b,a| {
    let v = b.1.cmp(&a.1);
    if v == Ordering::Equal {
      b.0.cmp(&a.0)
    } else {
      v
    }
  });
  
  let mut map:HashMap<usize, usize> = HashMap::new();
  for i in 0..n {
    map.insert(vis[i].0, i);
  }
  
  for i in 0..n {
    let ti = *map.get(&i).unwrap();
    let v = vis.remove(ti);
    println!("{}", vis[n/2 - 1].1);
    vis.insert(ti, v);
  }
}