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<cmath>
#include<algorithm>
#include<vector>
#include<functional>
#include<string>
#include<iomanip>
#include<map>
#include<utility>
#include<string>

template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }

using namespace std;

#define min_3(a, b, c) min(a, min(b, c))
#define max_3(a, b, c) max(a, max(b, c))
typedef long long ll;


int main()
{
    int n; cin >> n;
    vector<int> x(n + 1);
    vector<int> y(n + 1);
    for(int i = 1; i <= n; i++){
        cin >> x[i];
    }

    copy(x.begin(), x.end(), y.begin());
    sort(y.begin(), y.end());

    for(int i = 1; i <= n; i++){
        if(x[i] <= y[n/2]){
            cout << y[n/2 + 1] << endl;
        }
        else{
            cout << y[n/2] << endl;
        }
    }
}