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 <bits/stdc++.h>
#define rep(i, n) for(long long int i = 0; i < n; i++)
#define _rep(i, m, n) for(long long int i = m; i < n; i++)
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
const int N = 1000000;
const ll mod = 1000000007;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};

ll gcd(ll A, ll B){
    if(B == 0)return A;
    return gcd(B, A % B);
}
ll lcm(ll A, ll B){
    return A * B / gcd(A, B);
}

/*------------------------------------------------------------------*/


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