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 ConsoleApplication11
{
    class Program
    {
        static void Main(string[] args)
        {
            double n = double.Parse(Console.ReadLine());
            string[] x = Console.ReadLine().Split(' ');
            string[] y = Console.ReadLine().Split(' ');
            for(int j = 0; j < 3; j++)
            {
                double Pn = 0;
                double Ans = 0;
                double p = j + 1;
                for (int i = 0; i < n; i++)
                {
                    double xn = double.Parse(x[i]);
                    double yn = double.Parse(y[i]);
                    double xxx = Math.Abs(xn - yn);
                    double aaa = Math.Pow(xxx, p);
                    Pn += aaa;
                }
                Ans = Math.Pow(Pn, 1 / p);
                Console.WriteLine(Ans);
            }
            //
            double sum = 0;
            for (int i = 0; i < n; i++)
            {
                double xn = double.Parse(x[i]);
                double yn = double.Parse(y[i]);
                double xxx = Math.Abs(yn - xn);
                sum = Math.Max(xxx,sum);
            }
            Console.WriteLine(sum);
        }
    }
}