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: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.IO;
using System.Linq;
using System.Diagnostics;
using System.Globalization;
using static System.Console;
using static System.Math;


namespace abc94_c
{
    class Program
    {
        static void Main(string[] args)
        {
            int s = int.Parse(ReadLine());
            List<int> list = new List<int>();
            list = ReadLine().Split().Select(int.Parse).ToList();

            for(int i=0; i<s; i++)
            {
                var tmp = new List<int>(list);
                tmp.RemoveAt(i);
                WriteLine(tmp.Median());
            }
        }
    }

    public static class LINQExtension
    {
        public static double Median(this IEnumerable<int> source)
        {
            if (source.Count() == 0)
            {
                throw new InvalidOperationException("Cannot compute median for an empty set.");
            }

            var sortedList = from number in source
                             orderby number
                             select number;

            int itemIndex = (int)sortedList.Count() / 2;

            if (sortedList.Count() % 2 == 0)
            {
                // Even number of items.
                return (sortedList.ElementAt(itemIndex) + sortedList.ElementAt(itemIndex - 1)) / 2;
            }
            else
            {
                // Odd number of items.
                return sortedList.ElementAt(itemIndex);
            }
        }
    }
}