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)

#pragma warning(disable:4996)
#include "bits/stdc++.h"
using namespace std;

using ll = long long;

#define REP(i, n) for(int i = 0;i < n;i++)
#define REPR(i, n) for(int i = n;i >= 0;i--)
#define FOR(i, m, n) for(int i = m;i < n;i++)
#define pb push_back
#define mp make_pair
#define fill(x,y) memset(x,y,sizeof(x))
#define even(x) x % 2 == 0
#define odd(x) x % 2 != 0
#define all(x) x.begin(), x.end()
#define pcnt __builtin_popcount
#define buli(x) __builtin_popcountll(x)
#define F first
#define S second
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );

int qp(int a, ll b, int mo) { int ans = 1; do { if (b & 1)ans = 1ll * ans*a%mo; a = 1ll * a*a%mo; } while (b >>= 1); return ans; }
int gcd(int a, int b) { return b ? gcd(b, a%b) : a; }
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };

template<typename T>
vector<T> make_v(size_t a) { return vector<T>(a); }

template<typename T, typename... Ts>
auto make_v(size_t a, size_t b, Ts... ts) {
	return vector<decltype(make_v<T>(b, ts...))>(a, make_v<T>(b, ts...));
}
template<typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type
fill_v(T &t, const V &v) { t = v; }
template<typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type
fill_v(T &t, const V &v) {
	for (auto &e : t) fill_v(e, v);
}
// auto dp = make_v<int>(4, h, w);
// fill_v(dp, 0);

const ll INF_LL = (1ll << 60);
const int INF_INT = (int)1e9;
const ll MOD_CONST = (ll)(1e9 + 7);

template<class T>bool chmax(T &a, const T &b) { if (a<b) { a = b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a = b; return 1; } return 0; }

inline tuple<ll, ll> rotate45(tuple<ll, ll> p)
{
	ll x = get<0>(p), y = get<1>(p);
	return tuple<ll, ll>(x + y, x - y);
}

int main(void)
{
	cin.tie(0); ios::sync_with_stdio(0); cout << fixed << setprecision(20);

	int N; cin >> N;
	set<int> num;
	multiset<int> as;
	vector<int> nums(N);
	REP(i, N) {
		int a; cin >> a;
		as.insert(a);
		num.insert(a);
		nums[i] = a;
	}

	map<int, int> rel;
	auto itr = num.begin();
	REP(i, num.size()) {
		int a = *itr;
		as.erase(as.find(a));

		//auto itr = as.begin();
		//if (as.size() > 1) advance(itr, (as.size() + 1) / 2 - 1);
		rel[a] = *next(as.begin(), (as.size() + 1) / 2 - 1);

		as.insert(a);
		++itr;
	}

	REP(i, N) {
		cout << rel[nums[i]] << endl;
	}
	
	return 0;
}