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 ITP1_10_D
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            string[] Xdata = Console.ReadLine().Split(' ');
            string[] Ydata = Console.ReadLine().Split(' ');
            int[] Xnumbers = new int[n];
            int[] Ynumbers = new int[n];
            double[] result = new double[n];

            for (int i = 0; i < n; i++)                       　　　   //要素を数字に変換
            {
                Xnumbers[i] = int.Parse(Xdata[i]);
                Ynumbers[i] = int.Parse(Ydata[i]);
                result[i] = Math.Abs(Xnumbers[i] - Ynumbers[i]);
            }

            double Dxy1 = 0;
            for (int i = 0; i < n; i++)                                //p=1のとき
            {
                Dxy1 += result[i];                                     
            }

            double sum2 = 0;
            for (int i = 0; i < n; i++)                               //p=2のとき
            {
                double square = Math.Pow(result[i], 2);
                sum2 += square;
            }
            double Dxy2 = Math.Sqrt(sum2);

            double sum3 = 0;
            for (int i = 0; i < n; i++)                               //p=3のとき
            {
                double square = Math.Pow(result[i], 3);
                sum3 += square;
            }
            double Dxy3 = Math.Pow(sum3, 1.0 / 3.0);

            double Dxy4 = 0;
            for (int i = 0; i < n; i++)                              //p=∞のとき
            {
                if (Dxy4 < result[i])
                    Dxy4 = result[i];
            }

            Console.WriteLine("{0:F8}", Dxy1);
            Console.WriteLine("{0:F8}", Dxy2);
            Console.WriteLine("{0:F8}", Dxy3);
            Console.WriteLine("{0:F8}", Dxy4);
        }
    }
}