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>

using namespace std;

typedef struct {
	int num;
	int index;
} NwI;

void msort(vector<NwI> &vec, int left, int right);
void merge(vector<NwI> &vec, int left, int mid, int right);


int main() {
	int N;
	vector<NwI> input;
	vector<int> medians;

	cin >> N;
	medians.resize(N);
	input.resize(N);

	for (int i = 0; i < N; i++) {
		cin >> input[i].num;
		input[i].index = i;
	}

	msort(input, 0, N - 1);

	for (int i = 0; i < N; i++) {
		if (i < N / 2) {
			medians[input[i].index] = input[N / 2].num;
		} else {
			medians[input[i].index] = input[N / 2 - 1].num;
		}
	}

	for (int i = 0; i < N; i++) {
		cout << medians[i] << "\n";
	}
	cout << flush;

	return 0;
}

void msort(vector<NwI> &vec, int left, int right) {
	if (left < right) {
		int m = (left + right) / 2;

		if (m >= left) msort(vec, left, m);
		if (m+1 <= right) msort(vec, m+1, right);

		merge(vec, left, m, right);
	}
}

void merge(vector<NwI> &vec, int left, int mid, int right) {
	vector<NwI> v;
	int i, j;

	i = left;
	j = mid + 1;

	while (i <= mid and j <= right) {
		if (vec[i].num < vec[j].num) {
			v.push_back(vec[i]);
			i++;
		} else {
			v.push_back(vec[j]);
			j++;
		}
	}

	if (i <= mid) {
		while (i <= mid) {
			v.push_back(vec[i]);
			i++;
		}
	}

	if (j <= right) {
		while(j <= right) {
			v.push_back(vec[j]);
			j++;
		}
	}

	for (int c = 0; c <= (right - left); c++) {
		vec[left + c] = v[c];
	}
}