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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n=sc.nextInt();
        int[][] nums=new int[n][3];
        for(int i=0;i<n;i++){
            nums[i][0]=sc.nextInt();
            nums[i][1]=i;
        }
        Comp comp=new Comp();
        comp.set_index(0);
        Arrays.sort(nums,comp);
        for(int i=0;i<n;i++){
            nums[i][2]=i<n/2?nums[n/2][0]:nums[n/2-1][0];
        }
        comp.set_index(1);
        Arrays.sort(nums,comp);
        for(int i=0;i<n;i++)System.out.println(nums[i][2]);
    }
}
class Comp implements Comparator {

    int index = 0;

    void set_index (int i) {
        index = i;
    }
    
    @Override
    public int compare (Object a, Object b) {
        int[] int_a = (int[]) a;
        int[] int_b = (int[]) b;
        return (int_a[index] - int_b[index]);
    }

}