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 (2.13.1) (judge verdict: Accepted)

import java.io.{BufferedOutputStream, BufferedReader, InputStreamReader, PrintWriter}
import java.lang

import scala.annotation.tailrec
import scala.collection.mutable.ArrayBuffer
import scala.reflect.ClassTag

object Main {
  def get[T: ClassTag](implicit in: BufferedReader, converter: String => T): T = {
    converter(in.readLine)
  }

  def getArray[T: ClassTag](implicit in: BufferedReader, converter: String => T): Array[T] = {
    get[String].split("\\s+").map[T](converter)
  }

  implicit val idConverter: String => String = s => s
  implicit val intConverter: String => Int = s => Integer.parseInt(s)
  implicit val longConverter: String => Long = s => lang.Long.parseLong(s)

  def get[T1, T2](
                   implicit in: BufferedReader,
                   converter1: String => T1,
                   converter2: String => T2
                 ): (T1, T2) = {
    getArray[String] match {
      case Array(v1, v2) => (converter1(v1), converter2(v2))
    }
  }

  def get[T1, T2, T3](
                       implicit in: BufferedReader,
                       converter1: String => T1,
                       converter2: String => T2,
                       converter3: String => T3
                     ): (T1, T2, T3) = {
    getArray[String] match {
      case Array(v1, v2, v3) => (converter1(v1), converter2(v2), converter3(v3))
    }
  }

  def get[T1, T2, T3, T4](
                           implicit in: BufferedReader,
                           converter1: String => T1,
                           converter2: String => T2,
                           converter3: String => T3,
                           converter4: String => T4
                         ): (T1, T2, T3, T4) = {
    getArray[String] match {
      case Array(v1, v2, v3, v4) => (converter1(v1), converter2(v2), converter3(v3), converter4(v4))
    }
  }

  implicit class TimesInt(val n: Int) {
    def times(f: Int => Unit): Unit = {
      for (i <- 0 until n) {
        f(i)
      }
    }
  }

  def primes(n: Long): ArrayBuffer[Long] = {
    val buf = ArrayBuffer.empty[Long]
    val s = Math.sqrt(n).toInt

    var v = n
    for (i <- 2 to s) {
      if (v == 1 || v == 0) {
        return buf
      } else {
        while (v % i == 0) {
          buf.append(i)
          v /= i
        }
      }
    }
    if (v > s) {
      buf.append(v)
    }
    buf
  }

  def divisors(n: Int): ArrayBuffer[Int] = {
    val buf = ArrayBuffer.empty[Int]
    val s = Math.sqrt(n).toInt

    for (i <- 1 to s) {
      if (n % i == 0) {
        buf.append(i)
        if (i != n / i) {
          buf.append(n / i)
        }
      }
    }
    buf
  }

  @tailrec
  def gcd(a: Long, b: Long): Long = {
    val reminder = a % b
    if (reminder == 0) {
      b
    } else {
      gcd(b, reminder)
    }
  }

  def lcm(a: Long, b: Long): Long = {
    a / gcd(a, b) * b
  }

  def toBitArray(n: Int, width: Int): Array[Boolean] = {
    val buf = ArrayBuffer.fill(width)(false)

    @tailrec
    def inner(n: Int, i: Int): Array[Boolean] = {
      buf(i) = (n & 1) == 0
      if (i == 0) {
        buf.toArray
      } else {
        inner(n / 2, i - 1)
      }
    }

    inner(n, width - 1)
  }

  def modpow(n: Long, p: Long, m: Long): Long = {
    @tailrec
    def inner(n: Long, p: Long, acc: Long): Long = {
      if (p == 0) {
        acc
      } else if ((p & 1) == 0) {
        inner(n * n % m, p >> 1, acc)
      } else {
        inner(n * n % m, p >> 1, acc * n % m)
      }
    }

    inner(n % m, p, 1)
  }

  def main(args: Array[String]): Unit = {
    implicit val in: BufferedReader = new BufferedReader(new InputStreamReader(System.in))
    val out = new PrintWriter(new BufferedOutputStream(System.out))
    val n = get[Int]
    val xs = getArray[Int]

    val xsSorted = xs.sorted
    val median1 = xsSorted(n / 2 - 1)
    val median2 = xsSorted(n / 2)

    n.times { i =>
      out.println(
        if (xs(i) <= median1) {
          median2
        } else {
          median1
        }
      )
    }

    out.flush()
  }
}