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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Linq.Enumerable;
using static System.Math;

class Program
{
    static void Main()
    {
        var N = int.Parse(ReadLine());
        var X = ReadLine().Split(' ').Select(int.Parse).ToArray();

        var sortedX = X.OrderBy(x => x).ToArray();
        var medL = sortedX[N / 2];
        var medS = sortedX[N / 2 - 1];

        foreach (var x in X)
        {
            if(x <= medS)
                WriteLine(medL);
            else
                WriteLine(medS);
        }
    }
}

static class ArrayDeconstructExtensions
{
    public static void Deconstruct<T>(this T[] a, out T i1, out T i2) => (i1, i2) = (a[0], a[1]);
    public static void Deconstruct<T>(this T[] a, out T i1, out T i2, out T i3) => (i1, i2, i3) = (a[0], a[1], a[2]);
    public static void Deconstruct<T>(this T[] a, out T i1, out T i2, out T i3, out T i4) => (i1, i2, i3, i4) = (a[0], a[1], a[2], a[3]);
    public static void Deconstruct<T>(this T[] a, out T i1, out T i2, out T i3, out T i4, out T i5) => (i1, i2, i3, i4, i5) = (a[0], a[1], a[2], a[3], a[4]);
}