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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace CompetitiveProgCsLib
{
	class MainProg
	{
		static string R => Console.ReadLine();
		static int RI => int.Parse(R);
		static double RD => double.Parse(R);
		static int[] RIs => R.Split(' ').Select(int.Parse).ToArray();
		static double[] RDs => R.Split(' ').Select(double.Parse).ToArray();
		static void Out(object obj) => Console.WriteLine(obj);
		static void Outb(bool b) => Out(b ? "Yes" : "No");
		static void OutB(bool b) => Out(b ? "YES": "NO");

		static void Main(string[] args)
		{
			var N = RI;
			var x = RIs;
			var li = new List<int>(x);
			Array.Sort(x);
			for(int i = 0;i < N;i++)
			{
				if (li[i] < x[N / 2]) Out(x[N / 2]);
				else Out(x[N / 2 - 1]);
			}
		}
	}
}