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 <algorithm>
#include <iostream>
#include <utility>
#include <vector>

using namespace std;

int main() {
  int n;
  cin >> n;
  vector<pair<int, int>> x(n);
  for (int i = 0; i < n; i++) {
    int v;
    cin >> v;
    x[i] = make_pair(v, i);
  }
  sort(x.begin(), x.end());
  vector<int> m(n);
  for (int i = 0; i < x.size(); ++i) {
    int prev = x[i].second;
    m[prev] = i;
  }

  for (int i = 0; i < n; i++) {
    if (m[i] < n / 2) {
      cout << x[n / 2].first << endl;
    } else {
      cout << x[n / 2 - 1].first << endl;
    }
  }
  return 0;
}