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 <math.h>
#include <numeric>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <time.h>
#include <list>

using namespace std;
typedef long long ll;
#define rep(i,n) for(int i=0;i<(n);++i)
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define reps(x,c) for(auto x:c)
#define all(x) begin(x), end(x)
#define pb(a) emplace_back(a) 
#define mp(a,b) make_pair((a),(b))
#define pl pair<ll,ll>
#define INF 2147483600
#define MOD 1000000007
#define fi first
#define se second
#define dbg(x) cout << #x"="<< (x) << endl
#define dbgv(x) cout<<#x<<endl;reps(y,x){cout<<y<<" ";}cout<<endl

int main(){
  ll n;cin>>n;
  vector<ll> x(n),y;
  rep(i,n){
  	cin>>x[i];
  }
  y=x;
  sort(all(x));
  rep(i,n){
  	if(x[n/2]>y[i]){
  		cout<<x[n/2]<<endl;
  	}else{
  		cout<<x[n/2-1]<<endl;
  	}
  }
  return 0;
}