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;

namespace ConsoleApp_CS
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = CIn.ReadInt();
            var x = new long[n];
            var y = new long[n];
            for (var i=0;i < n; i++)
            {
                x[i] = CIn.ReadInt();
                y[i] = x[i];
            }

            Array.Sort(y);


            foreach(var item in x)
            {
                if (item < y[n / 2])
                {
                    Console.WriteLine(y[n / 2]);
                }
                else
                {
                    Console.WriteLine(y[n / 2 - 1]);
                }
            }

            
            
        }
    }

    class CIn
    {
        private static readonly Queue<string> fieldBuffer = new Queue<string>();

        public static string Read()
        {
            if (fieldBuffer.Count == 0)
            {
                foreach (var field in Console.ReadLine().Split())
                {
                    fieldBuffer.Enqueue(field);
                }
            }
            return fieldBuffer.Dequeue();
        }

        public static int ReadInt() => int.Parse(Read());
        public static long ReadLong() => long.Parse(Read());
        public static double ReadDouble() => double.Parse(Read());

        public static string[] ReadStringArray(long n)
        {
            var array = new string[n];
            for (var i = 0; i < n; i++)
            {
                array[i] = Read();
            }
            return array;
        }

        public static int[] ReadIntArray(long n)
        {
            var array = new int[n];
            for (var i = 0; i < n; i++)
            {
                array[i] = ReadInt();
            }
            return array;
        }

        public static long[] ReadLongArray(long n)
        {
            var array = new long[n];
            for (var i = 0; i < n; i++)
            {
                array[i] = ReadLong();
            }
            return array;
        }

        public static double[] ReadDoubleArray(long n)
        {
            var array = new double[n];
            for (var i = 0; i < n; i++)
            {
                array[i] = ReadDouble();
            }
            return array;
        }
    }
}