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::str::FromStr;
use std::fmt::Debug;
use std::cmp;

#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

struct UnionFind{
    v: Vec<usize>
}

impl UnionFind{
    fn new(n: usize) -> UnionFind{
        let mut v: Vec<usize> = Vec::new();
        for i in 0..n{
         v.push(i);
        }
        UnionFind{v:v}
    }

    fn find(&mut self, i: usize) -> usize{
        if self.v[i] == i{
            i
        }else{
            let ni = self.v[i];
            self.v[i] = self.find(ni);
            self.v[i]
        }
    }

    fn union(&mut self, i: usize, j: usize){
        let root_i = self.find(i);
        let root_j = self.find(j);
        self.v[root_i] = root_j;
    }

}

struct CombMod{
    fac: Vec<u64>,
    inv: Vec<u64>,
    finv: Vec<u64>,
    mmod: u64,
}

impl CombMod{
    pub fn new(max: u64, m: u64) -> CombMod{
        let max: usize = max as usize;
        let mut fac: Vec<u64> = vec![0;max+1];
        let mut finv: Vec<u64> = vec![0;max+1];
        let mut inv: Vec<u64> = vec![0;max+1];

        fac[0] = 1;
        fac[1] = 1;
        finv[0] = 1;
        finv[1] = 1;
        inv[1] = 1;

        for i in 2..max+1{
            fac[i] = fac[i-1] * i as u64 % m;
            inv[i] = m - inv[m as usize %i] * (m/(i as u64)) % m;
            finv[i] = finv[i-1] * inv[i] % m;
        }

        CombMod{
            fac: fac,
            finv: finv,
            inv: inv,
            mmod: m,
        }
    }

    fn get(&self, n: u64, m: u64) -> u64{
        assert!(n >= m && n != 0 && m != 0);
        self.fac[n as usize] * self.finv[m as usize] % self.mmod
            * self.finv[(n-m) as usize] % self.mmod
    }
}

fn main(){
    let n: usize = read_as_vec()[0];
    let x = read_as_vec::<u64>();

    let mut sorted_x = x.clone();
    sorted_x.sort();

    let mid_pos = n/2-1;
    let median = sorted_x[mid_pos];
    for i in 0..n{
        if median >= x[i]{
            println!("{}", sorted_x[mid_pos+1]);
        }else{
            println!("{}", sorted_x[mid_pos]);
        }
    }
}