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 = Integer.parseInt(scan.nextLine());
	String[] xs = scan.nextLine().split(" ");
	String[] ys = scan.nextLine().split(" ");
	int[] x = new int[n];
	int[] y = new int[n];
	for (int i = 0; i < n; i++) {
	    x[i] = Integer.parseInt(xs[i]);
	    y[i] = Integer.parseInt(ys[i]);
	}
	System.out.println(manhattanDistance(x, y));
	System.out.println(minkowskiDistance(x, y, 2));
	System.out.println(minkowskiDistance(x, y, 3));
	System.out.println(chebyshevDistance(x, y));
    }
    public static double absoluteValue(int a, int b){
	if (a < b) {
	    return (double)b - a;
	} else {
	    return (double)a - b;
	}
    }
    public static double manhattanDistance(int[] x, int[] y){
	double sum = 0;
	for (int i = 0; i < x.length; i++) {
	    sum += absoluteValue(x[i], y[i]);
	}
	return (double)sum;
    }
    public static double minkowskiDistance(int[] x, int[] y, int p){
	double sum = 0;
	for (int i = 0; i < x.length; i++) {
	    sum += Math.pow(absoluteValue(x[i], y[i]), p);
	}
	if (p == 2) {
	    return Math.sqrt(sum);
	} else if (p == 3) {
	    return Math.cbrt(sum);
	}
	return 0;
    }
    public static double chebyshevDistance(int[] x, int[] y){
	double max = 0;
	for (int i = 0; i < x.length; i++) {
	    double distance = absoluteValue(x[i], y[i]);
	    if (max < distance) {
		max = distance;
	    }
	}
	return max;
    }
}