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 Math_Functions
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            var input_x = Console.ReadLine().Split(' ');
            var input_y = Console.ReadLine().Split(' ');
            Int64[] x = new Int64[n];
            Int64[] y = new Int64[n];
            for (int i = 0; i < input_x.Length; ++i) x[i] = int.Parse(input_x[i]);
            for (int i = 0; i < input_y.Length; ++i) y[i] = int.Parse(input_y[i]);
            Int64 p1 = 0, p2 = 0, p3 = 0, ngo = 0;
            for (int i = 0; i < n; ++i)
            {
                Int64 work = Math.Abs(x[i] - y[i]);
                p1 += work;
                p2 += (int)Math.Pow(work, 2);
                p3 += (int)Math.Pow(work, 3);
                if (ngo < work) ngo = work;
            }
            Console.WriteLine(p1);
            Console.WriteLine(Math.Pow(p2, 1 / 2.0));
            Console.WriteLine(Math.Pow(p3, 1 / 3.0));
            Console.WriteLine(ngo);
        }
    }
}