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)

import scala.io.Source
import scala.math._

object Main{
  def main(args: Array[String]){
    val lines = for{
      in <- Source.stdin.getLines.toList
    }yield in.toString.split(" ").toList.map(_.toInt)

    println(dimDis(lines(1), lines(2), 1).sum)
    println(sqrt(dimDis(lines(1), lines(2), 2).sum))
    println(pow(dimDis(lines(1), lines(2), 3).sum, (1.0/3.0)))
    println(dimDis(lines(1), lines(2), 1).max)
  }

  def dimDis(from: List[Int], to: List[Int], n: Int): List[Double] ={
    if(from == Nil) List()
    else if(to == Nil) List()
    else pow(abs(from.head - to.head), n) :: dimDis(from.tail, to.tail, n)
  }
}