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.IO;
using System.Text.RegularExpressions;
using System.Text;
using System.Diagnostics;
using static System.Math;
using static System.Array;

//var input = Console.ReadLine().Split().Select(int.Parse).ToArray();
namespace AtCoderSolve
{

    class Solve
    {
        const int mod = 1000000007;
        const int INF = 2147483647;
        const long SINF = 9223372036854775807;

        static int N;
        static List<Tuple<int, int>> X;
        
        
        

        public static void Input()
        {
            var cin = new Scanner();
            N = int.Parse(Console.ReadLine());
            X = new List<Tuple<int, int>>(N);
            var input = cin.SplitReader();
            for(var i = 0; i < N; i++)
            {
                X.Add(new Tuple<int, int>(input[i], i));
            }
        }

        static void Main(string[] args)
        {
            Input();

            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            X.Sort();
            int[] ans = new int[N];
            for(var i = 0; i < N; i++)
            {
                if (i <= (N / 2) - 1)
                {
                    ans[X[i].Item2] = X[N / 2].Item1;
                }
                else
                {
                    ans[X[i].Item2] = X[(N / 2) - 1].Item1;
                }
            }

            for(var i = 0; i < N; i++)
            {
                Console.WriteLine(ans[i]);
            }

            Console.Out.Flush();

        }





    }

    public class Scanner
    {
        public int[] SplitReader()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] SplitReaderL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }

    }

    public class Graph
    {
        
    }
}