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.util.Scanner;
public class Main{
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        double [] x = new double[n];
        double [] y = new double[n];
        for(int a = 0; a < n; a++){
            x[a] = scan.nextDouble();
        }
        for(int a = 0; a < n; a++){
            y[a] = scan.nextDouble();
        }
        System.out.printf("%.6f\n", distance(x,y,1,n));
        System.out.printf("%.6f\n", distance(x,y,2,n));
        System.out.printf("%.6f\n", distance(x,y,3,n));
        System.out.printf("%.6f\n", distance(x,y,4,n));
    }
    public static double distance(double x[], double y[], int p, int n){
        double answer = 0;
        if(p == 4){
            double max = 0;
            for (int a = 0; a < n; a++){
                if(Math.abs(x[a] - y[a]) > max){
                    max = Math.abs(x[a] - y[a]);
                }
            }
            answer = max;

        }
        else if(p == 3){
            for (int a = 0; a < n; a++){
                answer = answer + Math.pow(Math.abs(x[a] - y[a]), p);
            }
            answer = Math.cbrt(answer);
        }
        else if(p == 2){
            for (int a = 0; a < n; a++){
                answer = answer + Math.pow(Math.abs(x[a] - y[a]), p);
            }
            answer = Math.sqrt(answer);

        }
        else{
            for (int a = 0; a < n; a++){
                answer = answer + Math.pow(Math.abs(x[a] - y[a]), p);
            }
            answer = Math.pow(answer, (1/p));
        }
        return answer;
    }
}