Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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 std = new Scanner(System.in);
		int n = Integer.parseInt(std.next());
		double vector_a[] = new double[n];
		for (int i=0; i<n; i++){
			vector_a[i] =  Double.parseDouble(std.next());
		}
		double vector_b[] = new double[n];
		for (int i=0; i<n; i++){
			vector_b[i] =  Double.parseDouble(std.next());
		}

		double dim1 = 0;
		for (int i=0; i<n; i++){
			dim1 += Math.abs(vector_a[i]-vector_b[i]);
		}

		double dim2 = 0;
		for (int i=0; i<n; i++){
			dim2 += Math.pow(Math.abs(vector_a[i]-vector_b[i]),2);
		}
		dim2 = Math.pow(dim2, 0.5);

		double dim3 = 0;
		for (int i=0; i<n; i++){
			dim3 += Math.pow(Math.abs(vector_a[i]-vector_b[i]),3);
		}
		dim3 = Math.pow(dim3, (1/3.0));

		double diminf = 0;
		for (int i=0; i<n; i++){
			diminf = Math.max(Math.abs(vector_a[i]-vector_b[i]),diminf);
		}

		System.out.println(String.format("%.5f", dim1));
		System.out.println(String.format("%.5f", dim2));
		System.out.println(String.format("%.5f", dim3));
		System.out.println(String.format("%.5f", diminf));
	}
}