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 num = int.Parse(Console.ReadLine());
            string[] inputx = Console.ReadLine().Split(' ');
            string[] inputy = Console.ReadLine().Split(' ');

            double D1 = 0;
            double D2 = 0;
            double D3 = 0;
            double D8 = 0;
            double dis1 = 0;
            double dis2 = 0;
            double dis3 = 0;
            double dis8 = 0;

            for (int i = 0; i < num; i++)
            {
                dis1 = Math.Abs(double.Parse(inputx[i]) - double.Parse(inputy[i]));
                D1 += dis1;
                dis2 += Math.Pow(dis1, 2);
                dis3 += Math.Pow(dis1, 3); 

                if (dis8 < dis1)
                {
                    dis8 = dis1;
                }
            }

            D2 = Math.Sqrt(dis2);
            D3 = Math.Pow(dis3, 1.0 / 3.0);
            D8 = dis8;

            Console.WriteLine("{0:f6}", D1);
            Console.WriteLine("{0:f6}", D2);
            Console.WriteLine("{0:f6}", D3);
            Console.WriteLine("{0:f6}", D8);
        }
    }
}