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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: Wrong Answer)

using System;

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

        int[] x = new int[n];
        int[] y = new int[n];
        string[] strX = Console.ReadLine().Split(' ');
        string[] strY = Console.ReadLine().Split(' ');

        for(int i =0;i<n;i++)
        {
            x[i] = int.Parse(strX[i]);
            y[i] = int.Parse(strY[i]);
        }
        Calc calc = new Calc();
        Console.WriteLine("{0:f8}",calc.Manhattan(x,y,n));
        Console.WriteLine("{0:f8}",calc.Euclid(x,y,n));
        Console.WriteLine("{0:f8}",calc.Minkowski(x,y,n));
        Console.WriteLine("{0:f8}",calc.Chebyshev(x,y,n));
    }
}

class Calc
{
    //p=3?????¨????????????????????????????????¢
    // Dxy = (?£^n i=1 |x_i - y_i|^p)^1/p
    public double Minkowski(int[] x, int[] y,int n)
    {
        double d2 = 0;
        for(int i=0;i<n;i++)
        {
            double d = Math.Abs(x[i] - y[i]);
            double d1 = Math.Pow(d, 3);
            d2 = d2 + d1;
        }
        double p = 0.33333333;
        double d3 = Math.Pow(d2, p); 
        return d3;
    }
    //p=1?????¨?????????????????????????????¢
    // Dxy = (|x_1-y_1|)^2+(|x_n-y_n|)^2
    public double Manhattan(int[] x,int[] y, int n)
    {
        double d1=0;
        for (int i = 0; i < n;i++ )
        {
            d1 += Math.Abs((double)x[i]-(double)y[i]);
        }
            return d1;
    }
    //p= 2?????¨?????????????????????????????¢
    // Dxy^2 =(| x_1 - y_1|)^2 + (| x_n - y_n|)^2 
    public double Euclid(int[] x, int[] y, int n)
    {
        double d2 = 0,d=0;
        for (int i = 0; i < n; i++)
        {
            double temp = Math.Abs((double)x[i] - (double)y[i]);
            d = d + Math.Pow(temp, 2);
        }
        d2 = Math.Sqrt(d);
        return d2;
    }
    //p= ????????¨???????????§????????§????????¢
    // Dxy = max^n i=1 (|x_i - y_i|)
    public double Chebyshev(int[] x, int[] y, int n)
    {
        double max = 0;
        for (int i = 0; i < n;i++ )
        {
            double temp = Math.Abs(x[i] - y[i]);
            if (temp > max)
                max = temp;
        }
            return max;
    }
}