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.IO;

namespace ABC094C
{
    class MainClass
    {
        public static void Main(string[] args)
        {
            string s1 = Console.ReadLine();
            string s2 = Console.ReadLine();

            int N = int.Parse(s1);
            string[] ss = s2.Split(' ');

            int[] wrk = new int[N];
            int[] num = new int[N];

            for (int i = 0; i < N; i++)
            {
                wrk[i] = int.Parse(ss[i]);
            }

            int cp = N / 2;

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

            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j < N; j++)
                {
                    if (i == j)
                    {
                        num[j] = 0;
                    }
                    else
                    {
                        num[j] = wrk[j];
                    }
                }

                Array.Sort(num);
                //Array.Reverse(num);

                Console.WriteLine(num[cp]);
            }

            Console.Out.Flush();
        }
    }
}