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 BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using System.Text;

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            var N = consoleReader.Int;
            var x = consoleReader.Split.Int;
            var sorted = (int[])x.Clone();
            Array.Sort(sorted);

            var middle1 = sorted[N / 2 - 1];
            var middle2 = sorted[N / 2];

            return AllLines(x.Select(i => i <= middle1 ? middle2 : middle1));
        }

        #region いつもの
        private readonly ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc()); static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
    }
#pragma warning disable
    public class ConsoleReader
    {
        private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries);
        private string[] line = Array.Empty<string>();
        private int linePosition;
        private TextReader textReader;
        public ConsoleReader(TextReader tr) { textReader = tr; }
        public int Int => int.Parse(String);
        public long Long => long.Parse(String);
        public double Double => double.Parse(String);
        public string String
        {
            get
            {
                if (linePosition >= line.Length)
                {
                    linePosition = 0;
                    line = ReadLineSplit();
                }
                return line[linePosition++];
            }
        }
        public class SplitLine
        {
            private string[] splited;
            public SplitLine(ConsoleReader cr) { splited = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); }
            public int[] Int => String.Select(x => int.Parse(x)).ToArray();
            public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray();
            public long[] Long => String.Select(x => long.Parse(x)).ToArray();
            public double[] Double => String.Select(x => double.Parse(x)).ToArray();
            public string[] String => splited;
        }
        public SplitLine Split => new SplitLine(this);
        public class RepeatReader : IEnumerable<ConsoleReader>
        {
            ConsoleReader cr; int count;
            public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; }
            public IEnumerator<ConsoleReader> GetEnumerator() => Enumerable.Repeat(cr, count).GetEnumerator();
            System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator();

            public IEnumerable<string> String => this.Select(cr => cr.String);
            public IEnumerable<int> Int => this.Select(cr => cr.Int);
            public IEnumerable<int> Int0 => this.Select(cr => cr.Int - 1);
            public IEnumerable<long> Long => this.Select(cr => cr.Long);
            public IEnumerable<double> Double => this.Select(cr => cr.Double);
        }
        public RepeatReader Repeat(int count) => new RepeatReader(this, count);
    }
    #endregion
}