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.

Constraints

* $1 \leq n \leq 100$
* $0 \leq x_i, y_i \leq 1000$

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.

Example

Input

3
1 2 3
2 0 4


Output

4.000000
2.449490
2.154435
2.000000
import java.util.Scanner;

public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int num = sc.nextInt();
        int[] xArray = new int[num];
        for(int i = 0; i < num; i++){
            xArray[i] = sc.nextInt();
        }
        int[] yArray = new int[num];
        for(int i = 0; i < num; i++){
            yArray[i] = sc.nextInt();
        }
        
        double[] p = new double[4];
        
        for(int i = 0; i < num; i++){
            double dif = Math.abs(xArray[i] - yArray[i]);
            p[0] += dif;
            p[1] += Math.pow(dif, 2);
            p[2] += Math.pow(dif, 3);
            p[3] = Math.max(p[3], dif);
            
        }
        p[1] = Math.sqrt(p[1]);
        p[2] = Math.cbrt(p[2]);
        
        for(double result: p){
            System.out.println(result);
        }
    }
}
