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.StdIn

object Main extends App {

  val n = StdIn.readLine().toInt
  val xs = StdIn.readLine().split(' ').map(_.toDouble)
  val ys = StdIn.readLine().split(' ').map(_.toDouble)
  
  def pat1(): Double = (xs zip ys).foldLeft(0D){ (acc, xy) =>
      acc + scala.math.abs(xy._1 - xy._2)
  }

  def pat2(): Double = (xs zip ys).foldLeft(0D){ (acc, xy) =>
    acc + scala.math.pow(scala.math.abs(xy._1 - xy._2), 2)
  }

  def pat3(): Double = (xs zip ys).foldLeft(0D){ (acc, xy) =>
    acc + scala.math.pow(scala.math.abs(xy._1 - xy._2), 3)
  }

  def patL(): Double = (xs zip ys).foldLeft(0D){ (acc, xy) =>
    if(acc > scala.math.abs(xy._1 - xy._2)) acc else scala.math.abs(xy._1 - xy._2)
  }

  val r1 = pat1()
  val r2 = scala.math.sqrt(pat2())
  val r3 = scala.math.cbrt(pat3())
  val rL = patL()

  println(f"$r1%.6f")
  println(f"$r2%.6f")
  println(f"$r3%.6f")
  println(f"$rL%.6f")
  
}