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 Python (3.4.3) (judge verdict: Runtime Error)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<ll> vi;
typedef pair<ll,ll> pi;
typedef pair<ll,pi> pii;
typedef vector<pi> vpi;
typedef set<ll> si;
typedef long double ld;
#define mp make_pair
#define pb push_back
#define f first
#define s second
ll INF = 1e18;
ll MOD = 1e9+7;
#define lb lower_bound
#define ub upper_bound
#define SZ(x) (ll)x.size()
#define ALL(x) x.begin(),x.end()
int l,r,A[100100], B[100100], N;

int main(){
  cin>>N;
  for (int i=0;i<N;++i){cin>>A[i];B[i] = A[i];}
  sort(A,A+N);
  l = A[N/2-1];
  r = A[N/2];
  for (int i=0;i<N;++i){
    if (B[i] <= l)cout<<r<<'\n';
    else cout<<l<<'\n';
  }
}