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;
namespace AOJ {
    internal class Program {
        public static void Main(string[] args) { new Program().solve(); }
        void solve() {
            var D = new Distance();
            int n = int.Parse(Console.ReadLine());
            var x = Console.ReadLine().Split().Select(v => double.Parse(v)).ToArray();
            var y = Console.ReadLine().Split().Select(v => double.Parse(v)).ToArray();
            if(x.Length != n || y.Length != n) return;//kuso
            Console.WriteLine(D.Manhattan(x, y));
            Console.WriteLine(D.Euclidean(x, y));
            Console.WriteLine(D.Minkowski(x, y, 3D));
            Console.WriteLine(D.Chebyshev(x, y));
        }
    }
    class Distance {
        private static Func <double, double, double> power = (value, p) => Math.Pow(value, p);
        private static Func <double, double, double> between = (x, y) => Math.Abs(y - x);
        //private Func <double[], double[], double[]> sequence=(xArr,yArr)=> xArr.Zip(yArr, (x, y) => between(x, y)).ToArray();
        private Func <double[], double[], double[]> sequence = (xArr, yArr) => {
            var ret = new double[xArr.Length];
            for(int i = 0; i < xArr.Length; ++i) { ret[i] = between(xArr[i], yArr[i]); }
            return ret;
        };
        public double Manhattan(double[] x, double[] y) { return sequence(x, y).Sum(); }
        public double Euclidean(double[] x, double[] y) {
            return power(sequence(x, y).Select(v => power(v, 2)).Sum(), 0.5);
        }
        public double Minkowski(double[] x, double[] y, double p) {
            return power(sequence(x, y).Select(v => power(v, p)).Sum(), 1 / p);
        }
        public double Chebyshev(double[] x, double[] y) { return sequence(x, y).Max(); }
    }
}