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)

#include <bits/stdc++.h>
using namespace std;

#define SORT(x) sort((x).begin(),(x).end())
#define RSORT(x) sort((x).begin(),(x).end(),greater<int>())
#define SZ(x) ((int)(x).size())
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define dump(x)  cout << #x << " = " << (x) << endl;
#define debug(x) cout << #x << " = " << (x) " (L" << __LINE__ << ") " << __FILE__ << endl;

typedef long long ll;
const int mod = 1e9+7;
const ll INF = 0x3f3f3f3f3f3f3f3f;
const int inf = 0x3f3f3f3f;

void solve()
{
  int n; cin>>n;
  vector<int> x(n, 0);
  for (int i=0; i<n; i++) {
    cin>>x[i];
  }
  for (int i=0; i<n; i++) {
    vector<int> y=x;
    y.erase(y.begin()+i);
    SORT(y);
    cout << y[n/2-1] << endl;
  }
}

int main()
{
  solve();
  return 0;
}