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;

public class Main {
	
	public static void main(String[] args) {
		try {

			BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
			String str = reader.readLine();
			int n = Integer.parseInt(str);
			str = reader.readLine();
			String[] vx = str.split(" ");
			str = reader.readLine();
			String[] vy = str.split(" ");
			
			double x = 0.0;
			double y = 0.0;
			double dist = 0.0;
			double[] exp = {1.0, 2.0, 3.0};
			double max = 0.0;
			double abs = 0.0;
			for (int j = 0; j < 3; j++) {
				for (int i = 0; i < n; i++) {
					x = Double.parseDouble(vx[i]);
					y = Double.parseDouble(vy[i]);
					abs = Math.abs(x - y);
					dist += Math.pow(abs, exp[j]);
					if (max < abs) {
						max = abs;
					}
				}
				System.out.println(Math.pow(dist, 1.0 / exp[j]));
				dist = 0.0;
			}
			System.out.println(max);
			
		} catch (IOException e) {
			e.printStackTrace();
		}
	}
}