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 Go (1.6) (judge verdict: Accepted)

package main

import (
  "fmt"
  "sort"
)

func main(){
  var N int
  fmt.Scan(&N)
  X := make([]int, N)
  for i:=0;i<N;i++{
    fmt.Scan(&X[i])
  }
  Y := make([]int,N)
  copy(Y,X)
  sort.Ints(X)
  // fmt.Println(X)
  // fmt.Println(Y)
  low := X[(N-1)/2]
  high := X[N/2]
  // fmt.Println(low,high)
  for i:=0;i<N;i++{
    if Y[i] <= low{
      fmt.Println(high)
    }else{
      fmt.Println(low)
    }
  }
}