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: Time Limit Exceeded)

#define REP(i, n) for (int i = 0; i < n; i++)
#define ALL(c) (c).begin(), (c).end()

#include <algorithm>
#include <cmath>
#include <iostream>
#include <vector>

using namespace std;

int medians(vector<int> X, int excluseP) {
  X.erase(X.begin() + excluseP);
  sort(ALL(X));
  int const center = X.size() / 2;
  return X[center];
}

int main() {
  int N;
  cin >> N;
  vector<int> X;
  REP(i, N) {
    int x;
    cin >> x;
    X.push_back(x);
  }

  REP(i, N) { cout << medians(X, i) << endl; }

  return 0;
}