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 Scala (2.11.7) (judge verdict: Wrong Answer)

object Main {
  def main(args: Array[String]): Unit = {
    val sc = new java.util.Scanner(System.in)
    
    val N = sc.nextInt()
    val X = Array.fill(N)(sc.nextInt())
    val SX = X.sorted
    val SXIdx = SX.zipWithIndex.toMap
    val medianL = X(N / 2 - 1)
    val medianR = X(N / 2)
    
    val r = new Array[Int](N)
    var i = 0
    while (i < N) {
      if (SXIdx(X(i)) < N / 2)
        r(i) = medianR
      else
        r(i) = medianL
      i += 1
    }
    println(r.mkString(" "))
  }
}