Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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.Linq;
using System.Collections.Generic;

class Test
{
    static void Main()
    {
        double n = double.Parse(Console.ReadLine());
        double[] x = Console.ReadLine().Split().Select(double.Parse).ToArray();
        double[] y = Console.ReadLine().Split().Select(double.Parse).ToArray();

        double D1 = 0;
        for (int i = 0; i < n; i++)
        {
            D1 += Math.Abs(x[i] - y[i]);
        }

        double D2 = 0;
        for (int i = 0; i < n; i++)
        {
            D2 += Math.Pow(x[i] - y[i], 2);
        }
        D2 = Math.Sqrt(D2);

        double D3 = 0;
        for (int i = 0; i < n; i++)
        {
            D3 += Math.Pow(Math.Abs(x[i] - y[i]), 3);
        }
        D3 = Math.Pow(D3, 1.0 / 3.0);

        double DI = 0;
        List<double> dd = new List<double>();
        for (int i = 0; i < n; i++)
        {
            dd.Add(Math.Abs(x[i] - y[i]));
            DI = dd.Max();
        }

        Console.WriteLine(D1);
        Console.WriteLine(D2);
        Console.WriteLine(D3);
        Console.WriteLine(DI);
    }
}