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;
namespace HelloWorld
{
    class Program
    {
        static void Main()
        {
            int[] Xvectors = new int[150];
            int[] Yvectors = new int[150];
            int n = int.Parse(Console.ReadLine());
            string[] line1 = Console.ReadLine().Split();
            string[] line2 = Console.ReadLine().Split();
            double p1sigma = 0;
            double p2sigma = 0;
            double p3sigma = 0;
            double pmaxsigma = 0;
            double three = 1;
            three = three / 3;
            for (int i = 0; i < line1.Length; i++)
            {
                Xvectors[i] = int.Parse(line1[i]);
                Yvectors[i] = int.Parse(line2[i]);
            }
            for (int i = 0; i < n; i++) p1sigma += Math.Abs(Xvectors[i] - Yvectors[i]);
            Console.WriteLine(p1sigma);
            for (int i = 0; i < n; i++) p2sigma += Math.Pow(Math.Abs(Xvectors[i] - Yvectors[i]), 2);
            Console.WriteLine(Math.Sqrt(p2sigma));
            for (int i = 0; i < n; i++) p3sigma += Math.Pow(Math.Abs(Xvectors[i] - Yvectors[i]), 3);
            Console.WriteLine(Math.Pow(p3sigma,three));
            //Console.WriteLine(Math.Cbrt(p3sigma));
            for (int i = 0; i < n; i++) pmaxsigma = Math.Max(pmaxsigma, Math.Abs(Xvectors[i] - Yvectors[i]));
            Console.WriteLine(pmaxsigma);
        }
    }
}