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: Wrong Answer)

#include<iostream>
#include<string>
#include<algorithm>
#include <string.h>
#include <stdio.h>
#include <math.h>
#include <set>
#include <queue>
#include <stack>
#include <map>

using namespace std;
typedef int status;
typedef long long ll;
typedef unsigned long long ull;
const ull base = 343;
const int INF = int(1e9);
const ll INF1 = ll(1e15);
const int MAX = 200002;

int N;
int a[MAX];

struct S{
    int x;
    int id;
}b[MAX];

bool cmp(S &a,S &b)
{
    if(a.x!=b.x){
        return a.x < b.x;
    }
    return a.id < b.id;
}

int main()
{

    cin>>N;
    for(int i = 1;i <= N;i++){
        cin>>a[i];
        b[i].x = a[i];
        b[i].id = i;
     }
    sort(b+1,b+1+N,cmp);

    for(int i = 1;i <= N;i++){
        int ti = N/2;
        if(b[ti].id!=i){
            if(b[ti].x<=a[i]){
                cout<<b[ti].x<<endl;
            }else{
                cout<<b[ti+1].x<<endl;
            }
        }else {
            cout<<b[ti+1].x<<endl;
        }
    }

    return 0;
}