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.IOException;
import java.util.Scanner;
public class Main {

	public static void main(String[] args) throws Exception {
		// TODO ?????????????????????????????????????????????
			Scanner sc = new Scanner(System.in);
			int a = sc.nextInt();
			double b=0,c=0,d=0,e=0;
			int x[]=new int[a];
			for(int z=0;z<a;++z){
				x[z] = sc.nextInt();
			}
			for(int z=0;z<a;++z){
				x[z] -= sc.nextInt();
				if(x[z]<0){
					x[z]=x[z]*-1;
				}
				if(e<x[z]){
					e=x[z];
				}
			}
			for(int z=0;z<a;++z){
				b = b + x[z];
			}
			
			for(int z=0;z<a;++z){
				c = c + Math.pow(x[z], 2);
			}
			c = Math.sqrt(c);
			for(int z=0;z<a;++z){
				d = d + Math.pow(x[z], 3);
			}
			d = Math.pow(d,(double)1/3);
			System.out.println(b);
			System.out.println(c);
			System.out.println(d);
			System.out.println(e);
	}

}