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 <string>
#include <tuple>
#include <cmath>
#include <queue>
#include <vector>
#include <map>
using namespace std;

#define ll int64_t
const long MOD = 1e9 + 7;


// 自作のソート関数
// 5で割った余りの大小で比較
bool less_second(const pair<int,long>& lhs, const pair<int,long>& rhs) {
    return lhs.second > rhs.second;
}


int main()
{
  long n;
  cin  >> n;
  std::vector<pair<int,long>> v(n);
  vector<long> r(n);
  for (int i = 0; i < n; ++i)
  {
     cin >>v[i].second; 
     v[i].first = i;
     r[i] = v[i].second;
  }
  sort(v.begin(), v.end(),less_second);


  int med = (v.size()+1)/2 - 1;
  // cout << "med"<<med <<endl;
  //  for (int i = 0; i < v.size(); ++i){
  //     cout << v[i].first << "-" << v[i].second << endl;
  //  }


  for (int i = 0; i < n; ++i){
    // cout <<"r:"<<r[i];
    if (v[med].second <= r[i] ){
      cout << v[med+1].second <<endl;
    }else{
      cout << v[med].second <<endl;
    }
    
  }
   

  return 0;
}