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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

int main(void){
	int N;
	cin>>N;
	vector<pair<int,int>> pairs;
	vector<int> numbers;

	for(int i=0;i<N;i++){
		int X;
		cin>>X;
		pair<int,int> temp = make_pair(i,X);
		pairs.push_back(temp);
		numbers.push_back(X);
	}
	
	sort(numbers.begin(),numbers.end());

	int candidate = numbers.at(N/2);
	int candidate_minus= numbers.at((N/2) -1);

	for(int i=0;i<N;i++){
		pair<int,int> temp = pairs.at(i);
		if(temp.second >= candidate){
			cout<<candidate_minus<<endl;
		}else{
			cout<<candidate<<endl;
		}
	}

	return 0;
}