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>
#include <set>
#include <algorithm>
#include <string>
#include <cmath>
#include <iomanip>
#include <map>
#include <set>
#include <numeric>
using namespace std;
#define loop(i,N) for(ll (i)=0; (i)<(N);++(i))
struct _OMAZINAI_ { _OMAZINAI_() { std::ios::sync_with_stdio(false); std::cin.tie(0); } } __omazinai_instance__;
#define INF ((1LL<<61) + (1<<29))
#define YesNo(x) {std::cout << ((x)?"Yes":"No") << std::endl;}
#define YESNO(x) {std::cout << ((x)?"YES":"NO") << std::endl;}
#define OddEven(x) {std::cout << ((x)%2?"Odd":"Even") << std::endl;}
#define ODDEVEN(x) {std::cout << ((x)%2?"ODD":"EVEN") << std::endl;}
typedef long long int ll;
ll my_gcd(ll a, ll b) { return b ? my_gcd(b, a%b) : a; };
void _INPUT_IMPL_() {};
template <class T, class... Args> void _INPUT_IMPL_(T& dest, Args&... args) { cin >> dest; _INPUT_IMPL_(args...); }
void _OUTPUT_IMPL_() {};
template <class T, class... Args> void _OUTPUT_IMPL_(T dest, Args... args) { cout << dest << (sizeof...(Args) ? " " : ""); _OUTPUT_IMPL_(args...); }
#define in(type, ...) type __VA_ARGS__; _INPUT_IMPL_(__VA_ARGS__)
#define in_v(type, name, cnt) vector<type> name(cnt); loop(i, cnt) cin >> name[i];
#define sort_v(v) std::sort(v.begin(), v.end())
#define unique_v(v) v.erase(std::unique(v.begin(), v.end()), v.end()) //必ずソート後に実行
#define out(...) (_OUTPUT_IMPL_(__VA_ARGS__), std::cout<<std::endl)
#define set_fix(x) ((std::cerr<<std::fixed<<std::setprecision(x)),(std::cout<<std::fixed<<std::setprecision(x)))
//小さい方に寄る
#define space_op(x, y, a, b, c) ([](auto x_, auto y_, auto a_, auto b_, auto c_){if(x_<y_)return a_;if(x_>y_)return c_;return b_;}(x,y,a,b,c))
#define space_out(x, y, a, b, c) out(space_op(x, y, a, b, c))

// ^^^ Template ^^^ //


int main() {
	in(ll, N);
	in_v(ll, X, N);
	decltype(auto) Xb = X;
	sort_v(X);
	loop(i, N)
		if (Xb[i] <= X[N / 2 - 1]) out(X[N/2]);
		else out(X[N / 2 - 1]);
	return 0;
}