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)

/**
  * http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_10_D&lang=jp
  * Math Functions - Distance II
  */
object Main {
  def main(args: Array[String]): Unit = {
    val n = io.StdIn.readInt()
    val x = io.StdIn.readLine().split(" ").map(_.toInt)
    val y = io.StdIn.readLine().split(" ").map(_.toInt)
    println(manhattanDistance(x, y))
    println(euclidDistance(x, y))
    println(minkowskiDistance(3, x, y))
    println(chebyshevDistance(x, y))
  }

  def minkowskiDistance(p: Int, x: Seq[Int], y: Seq[Int]): Double = {
    math.pow(
      (x zip y).foldLeft(0.0) {
        (acc, pair) => acc + math.pow(math.abs(pair._1 - pair._2), p)
      }, 1.0 / p)
  }

  def manhattanDistance(x: Seq[Int], y: Seq[Int]): Double = {
    minkowskiDistance(1, x, y)
  }

  def euclidDistance(x: Seq[Int], y: Seq[Int]): Double = {
    minkowskiDistance(2, x, y)
  }

  def chebyshevDistance(x: Seq[Int], y: Seq[Int]): Double = {
    (x zip y).map(pair => math.abs(pair._1 - pair._2)).max
  }

}