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: Time Limit Exceeded)

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

class Main{


	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);			//文字の入力
		int n = sc.nextInt();
		int[] x =new int[n];
		ArrayList<Integer> data = new ArrayList<Integer>();
		for(int i = 0;i < n;i++){
			x[i] = sc.nextInt();
			data.add(x[i]);
		}
		
		for(int i = 0;i < n;i++){
			ArrayList<Integer> xx = (ArrayList<Integer>)data.clone();
			xx.remove(i);
			Collections.sort(xx);
			System.out.println(xx.get((xx.size())/2));
//			System.out.println();
//			for(int j = 0;j < n;j++){
//				System.out.print (data.get(j)+" ");
//			}
//			System.out.println();

		}
		
		

	}





}

class UnionFind{
	int[] parent;
	public UnionFind(int N){
		this.parent = new int[N];
		for(int i = 0; i < N;i++){
			parent[i] = i;
		}
	}
	public int root(int x){			//根要素を取得
		if(parent[x] == x){			//初期状態
			return x;
		}else{
			return parent[x] = root(parent[x]);    	//再帰によって根を取得
		}
	}
	public void unite(int x,int y){ 	//統合メソッド
		if(same(x,y)){					//同じ根なら終了
			return;
		}
		int xroot = root(x);
		int yroot = root(y);
		parent[xroot] = yroot;			//統合
		return;

	}

	public boolean same(int x,int y){			//根が同じか（同じグループに属しているか）を判定
		return(root(x) == root(y));
	}
}



class Pair implements Comparable{
	int from;		//p
	int end;		//y
	int num;
	int bango;
	@Override
	public int compareTo(Object other) {
		Pair otherpair = (Pair)other;

		return end - otherpair.end;
	}
}