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) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        int[] x = convertStringToInt(br.readLine().split(" "));
        int[] y = convertStringToInt(br.readLine().split(" "));

        calcMD(x,y,1);
        calcMD(x,y,2);
        calcMD(x,y,3);
        calcMD(x,y,0);

        br.close();
    }

	private static int[] convertStringToInt(String[] str){
		int[] list = new int[str.length];
		for(int i=0; i<str.length;i++){
			list[i] = Integer.parseInt(str[i]);
		}
		return list;
	}


    private static void calcMD(int[] x, int[] y,int p){
    	double D=0;
    	if(p == 0){
    		for(int i=0;i<x.length;i++){
    			double d = Math.abs(x[i]-y[i]);
    			if(D<=d){
    				D=d;
    			}
    		}
    	}else{
    		double d=0;
    		for(int i=0;i<x.length;i++){
    			d += Math.pow(Math.abs(x[i] - y[i]), p);
    		}
			D  =Math.pow(d, (double)1/p);
    	}
    	System.out.println(D);
    }
}