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)

#define loop(i, s, e) for(ll i = s;i < e;i++)

#include <iostream>
#include <iomanip>
#include <set>
#include <vector>
#include <queue>
#include <stack>
#include <utility>
#include <algorithm>
#include <map>
#include <cmath>
//#include "vector2d.cpp"

using namespace std;
//using namespace libcgl;
typedef long long signed ll;

ll n,x[200000],xx[200000];

int main() {
    cin >> n;
    loop(i,0,n) {cin >> x[i];xx[i]=x[i];}
    sort(xx,xx+n);
    ll m = n / 2 - 1;
    loop(i,0,n) {
        if(x[i] <= xx[m]) cout << xx[m+1] << endl;
        else cout << xx[m] << endl;
    }
}