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 <iomanip>
#include <cstring>
#include <string>
#include <vector>
#include <random>
#include <bitset>
#include <queue>
#include <cmath>
#include <stack>
#include <set>
#include <map>
#define rep(i,n) for (int i=0; i<n;++i)
#define rep_down(i,n) for (int i=n-1; i>=0;--i)
typedef long long ll;
using namespace std;
const ll MOD = 1000000007LL;
int N;
typedef pair<int, int> P;
vector<P> X;
vector<P> Y;

int main() {
  cin.sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);

  cin >> N;
  int a;
  rep(i, N){
    cin >> a;
    P p = make_pair(a, i);
    X.push_back(p);
  }
  sort(X.begin(), X.end());

  int s_medi = X[N/2-1].first;
  int b_medi = X[N/2].first;

  rep(i, N){
    if(i<N/2){
      P p = make_pair(X[i].second, b_medi);
      Y.push_back(p);
    } else{
      P p = make_pair(X[i].second, s_medi);
      Y.push_back(p);
    }
  }

  sort(Y.begin(), Y.end());
  rep(i, N){
    cout << Y[i].second << endl;
  }

  return 0;
}