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 C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			var Instance = new Question();
			Instance.Exec();
		}
	}

	public class Question
	{
		public void Exec()
		{
			long n = long.Parse(Console.ReadLine());
			var vx = Console.ReadLine().Split(' ').Select(i => double.Parse(i)).ToArray();
			var vy = Console.ReadLine().Split(' ').Select(i => double.Parse(i)).ToArray();

			double[] distances = new double[4];
			double max = 0.0;
			for (var i = 0; i < n; ++i) {
				double diff = Math.Abs(vx[i] - vy[i]);
				distances[0] += diff;
				distances[1] += Math.Pow(diff, 2.0);
				distances[2] += Math.Pow(diff, 3.0);
				max = Math.Max(max, diff);
			}

			distances[1] = Math.Sqrt(distances[1]);
			distances[2] = Math.Pow(distances[2], 1.0 / 3.0);
			distances[3] = max;

			foreach (var item in distances) {
				Console.WriteLine($"{item:f6}");
			}
			
			Console.ReadKey();
		}
	}
}