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.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Distance_II
{
    class Program
    {
        static void Main(string[] args)
        {
            int times = int.Parse(Console.ReadLine());
            string[] line1 = Console.ReadLine().Split(' ');
            string[] line2 = Console.ReadLine().Split(' ');
            double[] nums1 = new double[times];
            double[] nums2 = new double[times];


            for (int i = 0; i < times; i++)
            {
                nums1[i] = double.Parse(line1[i]);
                nums2[i] = double.Parse(line2[i]);
            }

            double[] diff = nums1.Select((x, index) => Math.Abs(x - nums2[index])).ToArray();

            double r1 = diff.Sum();
            double r2 = Math.Sqrt(diff.Sum(x => Math.Pow(x, 2)));
            double r3 = Math.Pow(diff.Sum(x => Math.Pow(x, 3)), 1 / 3d);
            double r4 = diff.Max();

            Console.WriteLine("{0:f6}",r1);
            Console.WriteLine("{0:f6}",r2);
            Console.WriteLine("{0:f6}",r3);
            Console.WriteLine("{0:f6}",r4);


        }
    }
}