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<cstdio>
# include<algorithm>
using namespace std;

int main(void)
{
    std::ios::sync_with_stdio(false);
    int a[200003];
    int b[200003];
    int n;
    while(cin >> n && n!=0)
    {
        int i;
        for(i = 1; i <= n; ++i)
        {
            cin >> a[i];
            b[i] = a[i];
        }
        sort(a+1, a+n+1);
        int mid = (1+n)/2;
        //cout << mid << endl;
        //for(i = 1; i <= n; ++i)
        //cout << a[i] << " ";
        //cout << endl;
        for(i = 1; i <= n; ++i)
        {
            if(b[i] > a[mid])
                cout << a[mid] << endl;
            else if(b[i] < a[mid])
                cout << a[mid+1] << endl;
            else
                cout << a[mid+1] << endl;
        }
    }
    return 0;
}