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.InputStreamReader;
import java.lang.Math;
/*Question
/2????????????????????????????????????????????????????????????????????¢??§??¬???????????????????????????????????°???????????????????§?????????¨????????§????????????????????????
/????????§??????2?????? n ?¬???????????????? x={x1,x2,...,xn} ??¨ y={y1,y2,...,yn} ????????¢????¨????????????????????????????
/????????????????????????????????¢?????¬???????¨?????????¨?????¨??????????¬??????????????????????????????¢?????\????????????????????? 
/Dxy=(???i=1n|xi???yi|p)1p
/p=1 ?????¨??? 
/Dxy=|x1???y1|+|x2???y2|+...+|xn???yn|
/??¨?????????????????????????????????????????¢??¨?????°???????????? 
/p=2 ?????¨??? 
/Dxy=(|x1???y1|)2+(|x2???y2|)2+...+(|xn???yn|)2/
??¨???????????????????????¬?????????????????????????????????????????¢??????????????????
/p=??? ?????¨??? 
/Dxy=maxni=1(|xi???yi|)
/??¨???????????????????????§????????§????????¢??¨?????°????????????
/2?????? n ?¬???????????????????????????????????????§???p ??????????????? 1???2???3?????? ?????????????????????????????¢????±???????????????°????????????????????????????????????
*/

/*Input
/1???????????´??° n ????????????????????????
/2????????????????????? x ???????´? {x1,x2,...xn}
/3????????????????????? y ???????´? {y1,y2,...yn} ????????????????????§?????????????????????
/??\?????????????????´??°?????§??????
*/

public class Main {
	public static void main(String[] args) throws Exception{
		BufferedReader sc = new BufferedReader(new InputStreamReader(System.in));
		//????????¨
		StringBuffer b = new StringBuffer();
		/*????????¨
		????????????p=1,p=2,p=3,p=??????????´???¨
		*/
		double[] p = new double[4];
		/*??\?????¨
		/???????????´??°n?????£??\
		/????????????x?????????x??????????????????y?????????y???????´?
		*/
		int n = Integer.parseInt(sc.readLine());
		String[] st = sc.readLine().split(" ");
		int[] x = new int[st.length];
		for(int i = 0;i < st.length;i++){
			x[i] = Integer.parseInt(st[i]);
		}
		st = sc.readLine().split(" ");
		int[] y = new int[st.length];
		for(int i = 0;i < st.length;i++){
			y[i] = Integer.parseInt(st[i]);
		}
		/*p1????¨????
		abs???????????°?°????
		*/
		for(int i = 0;i < n;i++){
			p[0] += Math.abs(x[i]-y[i]);
		}
		/*p2????¨????
		p1?????????pow,sqrt???????????°??????
		*/
		for(int i = 0;i < n;i++){
			p[1] += Math.pow(Math.abs(x[i]-y[i]),2);
		}
		p[1] = Math.sqrt(p[1]);
		/*p3????¨????
		????´????p2??¨??????????????§????????????cbrt??¨3????????????
		*/
		for(int i = 0;i < n;i++){
			p[2] += Math.pow(Math.abs(x[i]-y[i]),3);
		}
		p[2] = Math.cbrt(p[2]);
		/*p=???????¨????
		max??§??????????????¨??????????????§????????????????????£??\???????????°??????
		*/
		for(int i = 0;i < n;i++){
			p[3] = Math.max(Math.abs(x[i]-y[i]),p[3]);
		}
		//????????????????????????
		for(double d:p)
			b.append(String.format("%.6f",d)).append("\n");
		System.out.println(b);
	}
}