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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;
public class Main
{
  public static void main(String args[])throws IOException
  {
    Scanner in=new Scanner(System.in);
    PrintWriter pw=new PrintWriter(System.out, true);
    int n=in.nextInt();
    ArrayList<Integer> arr=new ArrayList<>();
    int a[]=new int[n];
    for(int i=0;i<n;i++)
    {
      int num=in.nextInt();
      arr.add(num);
      a[i]=num;
    }
    Collections.sort(arr);
    for(int i=0;i<n;i++)
    {
      if(a[i]<=arr.get((n/2)-1))
      pw.println(arr.get(n/2));
      else
      pw.println(arr.get((n/2)-1))  ;
    //  arr.add(ind,a[i]);
    }
  }
}