Problem:
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Distance II

Your task is to calculate the distance between two $n$ dimensional vectors $x = \{x_1, x_2, ..., x_n\}$ and $y = \{y_1, y_2, ..., y_n\}$.

The Minkowski's distance defined below is a metric which is a generalization of both the Manhattan distance and the Euclidean distance.

\[
D_{xy} = (\sum_{i=1}^n |x_i - y_i|^p)^{\frac{1}{p}}
\]

It can be the Manhattan distance

\[
D_{xy} = |x_1 - y_1| + |x_2 - y_2| + ... + |x_n - y_n|
\]

where $p = 1 $.

It can be the Euclidean distance

\[
D_{xy} = \sqrt{(|x_1 - y_1|)^{2} + (|x_2 - y_2|)^{2} + ... + (|x_n - y_n|)^{2}}
\]

where $p = 2 $.

Also, it can be the Chebyshev distance

\[
D_{xy} = max_{i=1}^n (|x_i - y_i|)
\]

where $p = \infty$

Write a program which reads two $n$ dimensional vectors $x$ and $y$, and calculates Minkowski's distance where $p = 1, 2, 3, \infty$ respectively.

Input

In the first line, an integer $n$ is given. In the second and third line, $x = \{x_1, x_2, ... x_n\}$ and $y = \{y_1, y_2, ... y_n\}$ are given respectively. The elements in $x$ and $y$ are given in integers.

Output

Print the distance where $p = 1, 2, 3$ and $\infty$ in a line respectively.
The output should not contain an absolute error greater than 10-5.

Constraints

$1 \leq n \leq 100$

$0 \leq x_i, y_i \leq 1000$

Sample Input

3
1 2 3
2 0 4

Sample Output

4.000000
2.449490
2.154435
2.000000

Solution in Scala (judge verdict: Accepted)

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val n = sc.nextInt()
  val vectorX = List.fill(n)(sc.nextInt())
  val vectorY = List.fill(n)(sc.nextInt())
  calcAndPrint(vectorX, vectorY, 1.0)
  calcAndPrint(vectorX, vectorY, 2.0)
  calcAndPrint(vectorX, vectorY, 3.0)
  calcInfAndPrint(vectorX, vectorY)

  def calcAndPrint(v1: List[Int], v2: List[Int], p: Double): Unit = {
    println(f"${v1.zip(v2).map(e => (e._1 - e._2).abs.toString.toBigDecimal.power(p)).sum.root(p)}%.6f")
  }

  def calcInfAndPrint(v1: List[Int], v2: List[Int]): Unit = {
    println(f"${v1.zip(v2).map(e => (e._1 - e._2).abs).max}%.6f")
  }

  implicit class StringExtends(val s: String) extends AnyVal {
    def toBigDecimal = BigDecimal(s)
  }

  implicit class DoubleExtends(val d: Double) extends AnyVal {
    def toBigDecimal = BigDecimal(d)
  }

  implicit class BigDecimalExtends(val b: BigDecimal) extends AnyVal {

    import scala.math.pow

    def power(d: Double) = pow(b.toDouble, d).toBigDecimal

    def root(d: Double) = pow(b.toDouble, 1.0 / d).toBigDecimal
  }

}