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)

#include<iostream>
#include<vector>
#include<queue>
#include<unordered_map>
#include<map>
#include<set>
#include<unordered_set>
#include<algorithm>
#include<cmath>
#include<cassert>
#include<thread>
#include<future>
using namespace std;

#define INF 1e15+7
typedef long long ll;



int main(){
    int N;
    cin>>N;
    vector<ll>X(N);
    vector<ll>vec(N);
    for(int i=0;i<N;i++){
        cin>>X[i];
        vec[i]=X[i];
    }
    sort(vec.begin(),vec.end());
    vector<ll>B(N);
    ll l = vec[N/2-1];
    ll r = vec[N/2];
    for(int i=0;i<N;i++){
        if(X[i]<=l){
            B[i]=r;
        } else if(X[i]>=r){
            B[i]=l;
        }
        cout<<B[i]<<endl;
    }
    
}