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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)


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

public class Main {

	static Scanner scanner;
	public static void main(String[] args) {
	    scanner = new Scanner(System.in);

	    int N=gi();
	    long[] X1=new long[N];
	    long[] X2=new long[N];

	    for(int i=0; i<N;i++) {
	    	X1[i]=gl();
	    	X2[i]=X1[i];
	    }

	    Arrays.sort(X2);

	    long a1=X2[N/2 - 1];
	    long a2=X2[N/2];
	    for(int i=0; i<N;i++) {
	    	int index = Arrays.binarySearch(X2, X1[i]);
            if(index<N/2) {
            	System.out.println(a2);
            } else {
            	System.out.println(a1);
            }
	    }
	    //System.out.print(sum);
	}

	// 文字列として入力を取得
	public static String gs() {
		return scanner.next();
	}

	// intとして入力を取得
	public static int gi() {
		return Integer.parseInt(scanner.next());
	}

	// longとして入力を取得
	public static long gl() {
		return Long.parseLong(scanner.next());
	}

	// doubleとして入力を取得
	public static double gd() {
		return Double.parseDouble(scanner.next());
	}
}