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>
#include <vector>
#include <map>
#include <queue>
#include <deque>
#include <string.h>
#include <math.h>
typedef long long ll;
#define INF			100000
#define MAX(x, y)	(((x) > (y))? (x) : (y))
#define MIN(x, y)	(((x) < (y))? (x) : (y))
#define ABS(x)		(((x) < 0)? (-1*(x)) : (x))
#define SWAP
#define REP(i,x,y)	for (int (i)=(x);(i)<(y);(i)++)
#define REP_(i,x,y)	for ((i)=(x);(i)<(y);(i)++)
#define MEMCLR(X)	memset((X),0,sizeof((X)))

using namespace std;
typedef pair<int, int> Point;
typedef vector<vector<Point>> Graph;

int N,al,ar,m;

int main() {
	
	cin >> N;
	
	vector<int> a(N),b(N);
	
	REP(i,0,N) cin >> a[i],b[i]=a[i];

	sort(b.begin(), b.end());

	m = N/2-1;
	al = b[m];
	ar = b[m+1];
	
	REP(i,0,N) 
		if (a[i]<al) cout << ar << endl;
		else cout << al << endl;
	
	return 0;
}