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)

#![allow(non_snake_case)]
#![allow(unused_imports)]
use proconio::input;
// use std::cmp::max;
// use std::cmp::min;
use std::collections::HashMap;
// use std::collections::VecDeque;

fn main() {
    input! {
        N: usize,
        Xs: [i64; N],
    }

    let mut sorted_Xs: Vec<(i64, usize)> = Vec::new();
    for i in 0..N {
        let tpl = (Xs[i], i);
        sorted_Xs.push(tpl)
    }
    sorted_Xs.sort();

    let mut orig_ind_to_sorted_ind: HashMap<usize, usize> = HashMap::new();
    for sorted_ind in 0..N {
        let orig_ind = sorted_Xs[sorted_ind].1;
        orig_ind_to_sorted_ind.insert(orig_ind, sorted_ind);
    }

    let mid_ind: usize = (N - 2) / 2 + 1;
    for orig_ind in 0..N {
        let sorted_ind: usize = *orig_ind_to_sorted_ind.get(&orig_ind).unwrap();

        // if sorted_Xs[sorted_ind] < sorted_Xs[mid_ind] {
        if sorted_ind < mid_ind {
            println!("{}", sorted_Xs[mid_ind].0);
        } else {
            println!("{}", sorted_Xs[mid_ind - 1].0);
        }
    }
}