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 <algorithm>
#include <random>
#include <string>
#include <cmath>
#include <sstream>
#include <istream>
#include <iomanip>
#include <typeinfo>
#include <stack>
#include <map>

using namespace std;
typedef long long int ll;

int main(){

    ll N = 0;
    cin >> N;
    vector<pair<ll, ll > > a;
    //map<ll >

    for(ll i = 0; i < N; i++){
        ll in = 0;
        cin >> in;
        a.push_back(make_pair(in, i));
    }

    sort(a.begin(), a.end());

    vector<ll > ans(N);

    for(ll i = 0; i < N; i++){
        if(i < N / 2){
            //ans += a[N / 2 + 1];
            ans[a[i].second] = a[N / 2].first;
        }else{
            //ans += a[N / 2];
            ans[a[i].second] = a[N / 2 -1].first;
        }
    }

    //表示
    for(ll i = 0; i < N; i++){
        cout << ans[i] << endl;
    }

    //cout << ans << endl;



}