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 <bits/stdc++.h>
#include <assert.h>
using namespace std;
typedef long long ll;
typedef long double ld;
#define PB push_back
#define MP make_pair
#define MOD 1000000007LL
#define endl "\n"
#define fst first
#define snd second
const ll UNDEF = -1;
const ll INF=1e18;
template<typename T> inline bool chkmax(T &aa, T bb) { return aa < bb ? aa = bb, true : false; }
template<typename T> inline bool chkmin(T &aa, T bb) { return aa > bb ? aa = bb, true : false; }
typedef pair<ll,ll> pll;
typedef vector<ll> vll;
typedef pair<int,int> pii;
void solve(int n, vector<long long> inp){
	vector<pii> v; for (int i=0;i<n;i++) v.PB(MP(inp[i],i));
	sort(v.begin(),v.end());
	vector<int> vans; vans.resize(n);
	for (int i=0;i<n/2;i++) {
		vans[v[i].snd]=v[n/2].fst;
	}
	for (int i=n/2;i<n;i++) {
		vans[v[i].snd]=v[n/2-1].fst;
	}
	for (int i=0;i<n;i++) printf("%d\n",vans[i]);
}

int main(){	
	ios_base::sync_with_stdio(false); cin.tie(0);
	long long N;
	scanf("%lld",&N);
	vector<long long> X(N-1+1);
	for(int i = 0 ; i <= N-1 ; i++){
		scanf("%lld",&X[i]);
	}
	solve(N, X);
	return 0;
}