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.*;
import java.io.*;

public class Main{
	final static int MOD = 1000000007;
	final static int INF = 1000000000;

	public static void main(String[] args) throws IOException{
		NScanner sc = new NScanner(System.in);
		int n = sc.nextInt();
		int[] x = new int[n];
		double di1 = 0, di2 = 0, di3 = 0, diinf = 0;
		for(int i = 0; i < n; ++i)
			x[i] = sc.nextInt();
		for(int i = 0; i < n; ++i){
			x[i] = Math.abs(x[i] - sc.nextInt());
			di1 += x[i];
			di2 += x[i]*x[i];
			di3 += x[i]*x[i]*x[i];
			diinf = Math.max(diinf, x[i]);
		}
		System.out.printf("%.6f\n", di1);
		System.out.printf("%.6f\n", Math.sqrt(di2));
		System.out.printf("%.6f\n", Math.cbrt(di3));
		System.out.printf("%.6f\n", diinf);
	}

}

class NScanner{

	private BufferedReader br;
	private StringTokenizer tok;

	public NScanner(InputStream is) throws IOException{
		br = new BufferedReader(new InputStreamReader(is));
		getLine();
	}

	private void getLine() throws IOException{
		while(tok == null || !hasNext()){
			tok = new StringTokenizer(br.readLine());
		}
	}

	public boolean hasNext(){
		return tok.hasMoreTokens();
	}

	public String next() throws IOException{
		if(hasNext()){
			return tok.nextToken();
		}else{
			getLine();
			return tok.nextToken();
		}
	}

	public int nextInt() throws IOException{
		if(hasNext()){
			return Integer.parseInt(tok.nextToken());
		}else{
			getLine();
			return Integer.parseInt(tok.nextToken());
		}
	}

	public long nextLong() throws IOException{
		if(hasNext()){
			return Long.parseLong(tok.nextToken());
		}else{
			getLine();
			return Long.parseLong(tok.nextToken());
		}
	}

	public double nextDouble() throws IOException{
		if(hasNext()){
			return Double.parseDouble(tok.nextToken());
		}else{
			getLine();
			return Double.parseDouble(tok.nextToken());
		}
	}
}