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: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.Collections;
import java.util.NoSuchElementException;

public class Main {
	//FastScannerクラス、普通の Scannerクラスだとメモリと時間を大幅に喰らうので高速化する内部クラス。
	
	public static void main(String[]args) {
		FastScanner sc = new FastScanner(System.in);
		int N = Integer.valueOf(sc.next());
		Integer []x = new Integer[N];
		Integer []X = new Integer[N];
		
		for(int i = 0;i<N;i++) {
			x[i] = Integer.valueOf(sc.next());
			X[i] = x[i];
		}
		
		Arrays.sort(x,Collections.reverseOrder());//降順にソート
		
		for(int i = 0;i<N;i++) {
			//System.out.print(x[i]);
			//System.out.print(" ");
			//System.out.println(X[i]);
		}
		
		int num = (N-1+1)/2;
		
		for(int i = 0;i<N;i++) {
			if(X[i]<x[num-1])
				System.out.println(x[num-1]);
			else
				System.out.println(x[num-1+1]);
		}
		
		
	}
		
	
	
	static class FastScanner {
		 
		private final InputStream in;
		private final byte[] buffer = new byte[1024];
		private int ptr = 0;
		private int buflen = 0;
 
		public FastScanner(InputStream source) {
			in = source;
		}
 
		private boolean hasNextByte() {
			if (ptr < buflen) {
				return true;
			} else {
				ptr = 0;
				try {
					buflen = in.read(buffer);
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (buflen <= 0) {
					return false;
				}
			}
			return true;
		}
 
		private int readByte() {
			if (hasNextByte()) return buffer[ptr++];
			else return -1;
		}
 
		private static boolean isPrintableChar(int c) {
			return 33 <= c && c <= 126;
		}
 
		private void skipUnprintable() {
			while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
		}
 
		public boolean hasNext() {
			skipUnprintable();
			return hasNextByte();
		}
 
		public String next() {
			if (!hasNext()) throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (isPrintableChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
 
		public long nextLong() {
			if (!hasNext()) throw new NoSuchElementException();
			long n = 0;
			boolean minus = false;
			int b = readByte();
			if (b == '-') {
				minus = true;
				b = readByte();
			}
			if (b < '0' || '9' < b) {
				throw new NumberFormatException();
			}
			while (true) {
				if ('0' <= b && b <= '9') {
					n *= 10;
					n += b - '0';
				} else if (b == -1 || !isPrintableChar(b)) {
					return minus ? -n : n;
				} else {
					throw new NumberFormatException();
				}
				b = readByte();
			}
		}
	}

}