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 n = sc.nextInt();
		int[] X = new int[n];
		for(int i = 0; i < n; i++) {
			X[i] = sc.nextInt();
		}
		int[] Y = new int[n];
		for(int i = 0; i < n; i++) {
			Y[i] = sc.nextInt();
		}		
		
		for(int i = 1; i <= 3; i++) {
			System.out.println(dist(X, Y, n, i));
		}
		System.out.println(distInf(X, Y ,n));
		
		sc.close();
	}	
	
	static double dist(int[] X, int[] Y, int n, int p) {
		double D = 0;
		for(int i = 0; i < n; i++) {
			double d = Math.abs(X[i] - Y[i]);
			D += Math.pow(d, p);
		}
		switch(p) {
			case 1 :{
				return(D);
			}
			case 2 :{
				return(Math.sqrt(D));
			}
			case 3 :{
				return(Math.cbrt(D));
			}
			default :{
				return(-1);
			}
		}
	}
	
	static double distInf(int[] X, int[] Y, int n) {
		double D = X[0] - Y[0];
		for(int i = 0; i < n; i++) {
			D = Math.max(D, Math.abs(X[i] - Y[i]));
		}
		return(D);
	}

}

