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 java.util.Scanner

object Main extends App {

  def distance2() = {
    val sc = new Scanner(System.in)

    def nextInt() = sc.next.toInt

    val n = nextInt
    val xs = List.fill(n)(nextInt)
    val ys = List.fill(n)(nextInt)

    
    val manhattan = {
      var acc = 0.0
      for ((x, y) <- xs zip ys) 
        acc += math.abs(x - y)
      acc
    }

    val p2 = {
      var acc = 0.0
      for ((x, y) <- xs zip ys) 
        acc += (x - y) * (x - y)
      math.sqrt(acc)
    }

    val p3 = {
      var acc = 0.0
      for ((x, y) <- xs zip ys) {
        val d = math.abs(x - y)
        acc += d * d * d
      }
      math.cbrt(acc)
    }

    val chebyshev = {
      for ((x, y) <- xs zip ys)
      yield math.abs(x - y)
    }.max

    println(manhattan)
    println(p2)
    println(p3)
    println(chebyshev)
  }

  distance2()
}