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>
using namespace std;
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define ll long long
#define ull unsigned long long
#define ld long double
#define vl vector<long long>
#define vvl vector<vector<long long>>
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define rep2(i, s, n) for (ll i = (s); i < (ll)(n); i++)
#define rrep(i, x) for (ll i = ((ll)(x)-1); i >= 0; i--)
#define pll pair<long long,long long>
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define vvc vector<vector<char>>
#define vc vector<char>
#define vvb vector<vector<bool>>
#define vb vector<bool>
#define maxe(x) *max_element(all(x))
#define mine(x) *min_element(all(x))
#define Size(x) ((int)(x).size())
#define umap unordered_map
const long long INF = 1LL << 60;
const long double pi = 3.1415926535897932;
long long MOD = 1000000007;
int dx[4]={1,0,-1,0};
int dy[4]={0,1,0,-1};

    template<class T> inline bool chmin(T& a, T b) {
        if (a > b) {
            a = b;
            return true;
        }
        return false;
    }
    template<class T> inline bool chmax(T& a, T b) {
        if (a < b) {
            a = b;
            return true;
        }
        return false;
    }

//lis,modpow,uf,modncr,soinsubunkai,yakusurekkyo,gyakugen
//mint

    signed main(){
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
        ll N;
        cin>>N;
        vl X(N);
        vl C(N);
        rep(i,N){
            cin>>X[i];
            C[i]=X[i];
        }
        sort(all(C));
        ll r=C[N/2];
        ll l=C[N/2-1];
        rep(i,N){
            if(X[i]<=l){
                cout<<r<<endl;
            }else{
                cout<<l<<endl;
            }
        }
    }