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 JAVA (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {
    public static void main(String[] args) {
        try (BufferedReader in = new BufferedReader(new InputStreamReader(System.in))){
            int n = Integer.parseInt(in.readLine());
            double x[] = Arrays.stream(in.readLine().split(" ")).mapToDouble(Double::parseDouble).toArray();
            double y[] = Arrays.stream(in.readLine().split(" ")).mapToDouble(Double::parseDouble).toArray();

            double abs[] = new double[n];
            for (int i = 0; i < n; i++) {
                abs[i] = Math.abs(x[i] - y[i]);
            }

            double p1 = Arrays.stream(abs).sum();
            double p2 = Math.sqrt(Arrays.stream(abs).map(d -> Math.pow(d, 2)).sum());
            double p3 = Math.pow(Arrays.stream(abs).map(d -> Math.pow(d, 3)).sum(), 1.0 / 3.0);
            double pInf = Arrays.stream(abs).max().getAsDouble();

            System.out.printf("%.6f\n", p1);
            System.out.printf("%.6f\n", p2);
            System.out.printf("%.6f\n", p3);
            System.out.printf("%.6f\n", pInf);
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
}