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 <iostream>
#include <algorithm>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <list>

using namespace std;
#define rep(i, n) for(int i = 0; i < (int)(n); ++i)
typedef long long ll;
int main() {
    int n;
    cin >> n;
    vector<int> a(n),b(n);
    vector<pair<int, int>> nums;
    rep(i, n) {
        int ai;
        cin >> ai;
        a[i] = ai;
        b[i] = ai;
    }
    sort(a.begin(), a.end());
    int cnt = 1;
    rep(i, n-1) {
        if(a[i] != a[i+1]) {
            nums.push_back(make_pair(a[i], cnt));
            cnt = 1;
        } else{
            cnt += 1;
        }
    }

    nums.push_back(make_pair(a[n-1], cnt));

    rep(i, n) {
        int count = 0;
        int delNum = b[i];
        rep(j, nums.size()) {
            int num = nums[j].first;
            count += nums[j].second;
            if(delNum == num) count -= 1;
            if(count >= n/2) {
                cout << num << endl;
                break;
            }
        }
    }

}