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: Runtime Error)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
  public static void main(String[] args) throws Exception {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt()+1;  //道のり
    int M = sc.nextInt();    //料金所の数
    int X = sc.nextInt();    //スタート地点
    int[] place = new int[M]; //料金所の場所
    
    int PatternA = 0;
    int PatternB = 0;
    
    for(int i = 0 ; i < M ; i++){
      place[i] = sc.nextInt();
    }
    
    for(int i = X ; i < N ; i++){ //右側の料金所の数
      for(int j = 0 ; j < place.length ; j++){
        if(i == place[j]){
          PatternA++;
        }
      }
    }
    
    for(int i = X ; i >= 1 ; i--){
      for(int j = 0 ; j < place.length ; j ++){
        if(i == place[j]){
        PatternB++;
        }
      }
    }
    if(PatternA < PatternB){
      System.out.println(PatternA);
    }else{
      System.out.println(PatternB);
    }
  }
}