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.Collections.Generic;
using System.Linq;
using System.Text;

namespace ConsoleApplication23
{
    //ITP1_10-D

    class Distance
    {
        int v;
        int[] x, y;

        public Distance(int[] i,int[] j,int k)
        {
            x = i;
            y = j;
            v = k;
        }

        public double Dis(int a)
        {
            double sum = 0;
            for (int i = 0; i < v; ++i)
            {
                sum += Math.Pow(Math.Abs(x[i] - y[i]),a);
            }
            return sum;
        }
    }

    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());

            string[] x = Console.ReadLine().Split(' ');
            int[] xArray = Array.ConvertAll(x, int.Parse);

            string[] y = Console.ReadLine().Split(' ');
            int[] yArray = Array.ConvertAll(y, int.Parse);


            Distance p = new Distance(xArray,yArray,n);         //????????????????????????????????????

            double p1, p2, p3;

            p1 = p.Dis(1);                      //????????????????????????
            p2 = Math.Pow(p.Dis(2), 1.0 / 2.0);
            p3 = Math.Pow(p.Dis(3), 1.0 / 3.0);


            double max = Math.Abs(xArray[0] - yArray[0]);       //p = ????????¨???
            for (int i = 1; i < n; ++i)
            {
                max = Math.Max((Math.Abs(xArray[i] - yArray[i])), max);
            }

            Console.WriteLine("{0:f8}", p1);
            Console.WriteLine("{0:f8}", p2);
            Console.WriteLine("{0:f8}", p3);
            Console.WriteLine("{0:f8}", max);
        }
    }
}