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++ (GCC 9.2.1) (judge verdict: Accepted)


// <------------- Template -----------------------> //


#include<bits/stdc++.h>
using namespace std;

#define fastio 			ios::sync_with_stdio(0);	cin.tie(0); cout.tie(0);  cout<<fixed;  cout<<setprecision(2);
#define randomINT 		mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
#define	newl 			cout<<"\n"
#define DISP(as)		for(auto it : as) cout<<it<<" ";newl;
#define all(x)         	(x).begin(),(x).end()
#define mset(x,val)    	memset(x,val,sizeof(x))
#define newl           	cout<<"\n"
#define pb             	push_back
#define mp             	make_pair
#define f 				first
#define s 				second
#define dline          cerr<<"///REACHED///\n";
#define deb1(x)        cerr<<#x<<" = "<<x<<'\n';
#define deb2(x,y)      cerr<<'['<<#x<<','<<#y<<"] = "<<'['<<x<<','<<y<<']'<<'\n';
#define deb3(x,y,z)    cerr<<'['<<#x<<','<<#y<<','<<#z<<"] = "<<'['<<x<<','<<y<<','<<z<<']'<<'\n';
#define N 1000000007 // prime modulo value 
 
typedef long long 				ll;
typedef long double 			ld;
typedef vector<ll> 				vll;
typedef pair<ll , ll> 			pll;
typedef pair<ld, ld> 			pld;
typedef unordered_map<ll, ll> 	um;
typedef vector<pll> 			vpll;

const ll 	MAX5 	= 	1e+5 + 7;
const ll 	MAX7 	= 	1e+7 + 7;
const ll 	MAXN 	= 	2 * 1e18;
const ll   	INF   	=  	0x7f7f7f7f7f7f7f7f;
const int  	INFi 	=  	0x7f7f7f7f;
const ll 	MOD		=  	1e+9 + 7;

vll adj[MAX5]; ll visit[] = {};

// <------------- Declare Variables Here ------------> //

ll T = 1;
ll n, x, y, q, m;
string s, t, d;
ll sum = 0;
ll cou = 0;


// <------------- Implement Functions Here ----------> //



// <------------- Start of main() -------------------> //

void MAIN() {
	cin >> n;
	vll ans(n);
	vpll a(n+1);
	a[0] = {0,0};
	for(ll i=1;i<=n;i++) cin>>x, a[i]={x,i};
	sort(all(a));
	for(ll i=1;i<=n;i++) {
		if(2*i<=n) {
			ans[a[i].s-1] = a[n/2+1].f;
		}		
		else {
			ans[a[i].s-1] = a[n/2].f;
		}
	}
	for(ll i=0;i<n;i++) {
		cout<<ans[i];newl;
	}
}

int main() {
	fastio; randomINT;
	//cin>>T;
	while (T--) {
		MAIN();
	}
	return 0;
}