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;

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            string[] sx = Console.ReadLine().Split(' ');
            string[] sy = Console.ReadLine().Split(' ');
            int[] d = new int[n];
            double p1=0, p2=0, p3=0, p4=0;

            for(int i=0;i<n;i++)
            {
                d[i] = Math.Abs(int.Parse(sx[i]) - int.Parse(sy[i]));
                p1 += d[i];
                p2 += Math.Pow(d[i], 2);
                p3 += Math.Pow(d[i],3);
                p4 = (p4 > d[i]) ? p4 : d[i];
            }

            Console.WriteLine("{0:.000000}",p1);
            Console.WriteLine("{0:.000000}",Math.Sqrt(p2));
            Console.WriteLine("{0:.000000}",Math.Pow(p3,(double)1/(double)3));
            Console.WriteLine("{0:.000000}",p4);
        }
    }
}