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 <algorithm>
using namespace std;
typedef pair<int, int> pii;
const int MAXN = 200000 + 10;
int ret[MAXN];
pii items[MAXN];
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    int n; cin >> n;
    int val;
    for (int i = 0; i < n; i++) {
        cin >> val;
        items[i] = {val, i};
    }
    sort(items, items+n);
    for (int i = 0; i < n; i++) {
        int mid = n / 2;
        if (items[i].first >= items[mid].first) {
            mid--;
        }
        ret[items[i].second] = items[mid].first;
    }
    for (int i = 0; i < n; i++) {
        cout << ret[i] << '\n';
    }


    return 0;
}