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: Wrong Answer)

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

namespace AtCoder
{
    class Program
    {
        static void Main()
        {
            Solve();

            Console.ReadKey();
        }

        static void Solve()
        {
            var N = IO.GetInt();
            var X = IO.GetIntList().OrderByDescending(x => x).ToList();
            var bigB = X[N / 2];
            var smallB = X[N / 2-1];
            for(int i = 0; i < N; i++)
            {
                if (i <= N / 2) { Console.WriteLine(bigB); }
                else { Console.WriteLine(smallB); }
            }

            //Console.Write(ans);
        }
    }


    static class IO
    {
        static public string GetString() { return Console.ReadLine(); }
        static public int GetInt() { return int.Parse(Console.ReadLine()); }
        static public long GetLong() { return long.Parse(Console.ReadLine()); }
        static public List<string> GetStringList() { return Console.ReadLine().Split(' ').ToList(); }
        static public List<int> GetIntList() { return Console.ReadLine().Split(' ').Select(int.Parse).ToList(); }
        static public List<long> GetLongList() { return Console.ReadLine().Split(' ').Select(long.Parse).ToList(); }
        static public List<double> GetDoubleList() { return Console.ReadLine().Split(' ').Select(double.Parse).ToList(); }
        static public void WriteStrings<T>(IEnumerable<T> values) { foreach (var o in values) { Console.Write(o + " "); } }
    }
}