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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;

public class Main {

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    int arr[] = new int[N+1];
    int srt[] = new int[N+1];
    for(int i = 1; i<=N; i++){
      arr[i] = sc.nextInt();
      srt[i] = arr[i];
    }
    Arrays.sort(srt);
    for(int i = 1; i<=N; i++){
      if(arr[i] >= srt[N/2+1]){
        System.out.println(srt[N/2]); 
      }
      else{
        System.out.println(srt[N/2+1]); 
      }
    }
  }

}


/*

pre[i] = arr[1] + arr[2] + arr[3] + arr[4] + ... + arr[i]
The question for some l and r
arr[l] + arr[l+1] + arr[l+2] + ... + arr[r]
= 
pre[r] - pre[l-1]

pre[r]   = arr[1] + arr[2] + ... + arr[l-1] + arr[l] + arr[l+1] + ... + arr[r]
-
pre[l-1] = arr[1] + arr[2] + ... + arr[l-1]

*/