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: Wrong Answer)

#include<iostream>
#include<algorithm>

using namespace std;

int main()
{
	int n;
	cin >> n;
	int x[200001];
	for (int i = 0; i < n; i++) cin >> x[i];
	int c[200001];
	for (int i = 0; i < 200001; i++)c[i] = 0;
	for (int i = 0; i < n; i++)c[i] = x[i];

	sort(x, x + n);
	
	for (int i = 0; i < n; i++) {
		if (c[i] < x[n / 2 - 1])cout << x[n / 2] << endl;
		if (c[i] > x[n / 2])cout << x[n / 2 - 1] << endl;
		if (c[i] == x[n / 2 - 1])cout << x[n / 2] << endl;
		if (c[i] == x[n / 2])cout << x[n / 2 - 1] << endl;
	}

	return 0;
}