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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Collections;
using System.Collections.Generic;

public class E512IO {
    private string[] reads;
    private int index;
    public E512IO() {
        Console.SetOut( new StreamWriter(Console.OpenStandardOutput()));
        this.reads = new string[0];
        this.index = 0;
    }
    ~E512IO() { Console.Out.Flush(); }
    private string Next () {
        this.index += 1;
        if (this.index > this.reads.Length) {
            this.reads = Console.ReadLine().Split();
            this.index = 0;
        }
        return this.reads[this.index];
    }
    private string[] NextLines () {
        this.reads = Console.ReadLine().Split();
        this.index = this.reads.Length;
        return this.reads;
    }
    
    public List<int> NextIntList() { return this.NextLines().Select(x => int.Parse(x)).ToList(); }
    public List<long> NextLongList() { return this.NextLines().Select(x => long.Parse(x)).ToList(); }
    public List<double> NextDoubleList() { return this.NextLines().Select(x => double.Parse(x)).ToList(); }
    public List<string> NextStringList() { return this.NextLines().ToList(); }
    public int NextInt() { return int.Parse(this.Next()); }
    public long NextLong() { return long.Parse(this.Next()); }
    public double NextDouble() { return double.Parse(this.Next()); }
    public string NextString() { return this.Next(); }
}

public class Program {
    static void Main (string[] args) {
        E512IO io = new E512IO();
        var n = io.NextInt();
        
        int[] a = io.NextIntList().ToArray();
        int[] t = a.ToArray();
        Array.Sort(t);
        int m = n / 2 - 1;
        for (int i = 0; i < n; ++i) {
            if (a[i] <= t[m]) {
                Console.WriteLine(t[m+1]);
            } else {
                Console.WriteLine(t[m]);
            }
        }
    }
}