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: Runtime Error)

#include<iostream>
#include<set>
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define rep1(i, n) for(int i = 1; i < (int)(n); i++)

#include <algorithm>
using namespace std;
#include <cmath>
#include <string>
#include<vector>
#define elif else if
typedef long long ll;
#define TENNINE 1000000005
#define TENFIVE 100005
int N;

int main(){

    cin >>N;
    ll X[TENNINE];
    ll y[TENNINE];
    // vector<ll>vc;
    rep(i,N){
        cin>>X[i];
        y[i] = X[i];
    }
    sort(y,y+N);

    rep(i,N){
        if(X[i]<=y[N/2 - 1]) cout<<y[N/2]<<endl;
        else cout<<y[N/2 -1]<<endl;   
    
    }
    
    return 0;

}