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 <string>
#include <algorithm>
#include <cmath>
#include <vector>
#include <numeric>
#include <set>
#include <cstdlib>
#include <queue>

using namespace std;

typedef long long llint;
typedef long double ld;
#define inf 1e18

priority_queue<llint,vector<llint>,greater<llint>> que;
priority_queue<llint> q;
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

llint n;
llint x[200005],tmp[200005];

void solve(){
	cin >> n;
	for(int i=0;i<n;i++){
		cin >> x[i];
		tmp[i]=x[i];
	}
	sort(x,x+n);
	int a=n/2-1;
	int b=n/2;
	llint c1=x[a];
	llint c2=x[b];
	for(int i=0;i<n;i++){
		if(tmp[i]==c1)cout << c2 << endl;
		else if(tmp[i]==c2)cout << c1 << endl;
		else cout << c2 << endl;
	}

}

int main(int argc, char *argv[]) {
  solve();
  return 0;
}