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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.Scanner;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Iterator;
import java.util.Collections;
import java.util.Comparator;

class Numbers{
        private int N;
        ArrayList<Integer> X = new ArrayList<Integer>();
        ArrayList<Integer> Y = new ArrayList<Integer>();
        Numbers(int n){ this.N = n; }

        Scanner scan = new Scanner(System.in);

        public void setX(){
                for(int i=0;i<N;i++){
                        this.X.add(scan.nextInt());
                        this.Y.add(this.X.get(i));
                }
                Collections.sort(this.Y);
        }
        public void checkY(){
                System.out.println("--- check Y ---");
                for(int i=0;i<this.getN();i++){
                        System.out.println(this.Y.get(i));
                }
                System.out.println("---------------");
        }

        public void Bi(){
                for(int i=0; i<this.getN(); i++){
                        if(this.X.get(i) > this.Y.get(this.getN() / 2 - 1)){
                                System.out.println(this.Y.get(this.getN() / 2 - 1));
                        }else{
                                System.out.println(this.Y.get(this.getN() / 2));
                        }
                }
        }
        public int getN(){ return this.N; }
}

class Main{
        public static void main(String args[]){
                Scanner scan = new Scanner(System.in);
                Numbers numbers = new Numbers(scan.nextInt());
                numbers.setX();
                //numbers.checkY();
                numbers.Bi();
        }
}