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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Drawing;
using System.IO;
using System.Linq;
using System.Text.RegularExpressions;
using System.Text;

namespace Fish.aizu
{
	public static class AizuOnlineJudge
	{
		public static int[] SplitToInts(string line)
		{
			return line.Split(' ').Select(x => int.Parse(x)).ToArray();
		}
		public static double[] SplitToDoubles(string line)
		{
			return line.Split(' ').Select(x => double.Parse(x)).ToArray();
		}
		public static long[] SplitToLongs(string line)
		{
			return line.Split(' ').Select(x => long.Parse(x)).ToArray();
		}
		public static int Main()
		{
			Compute(Console.In, Console.Out);
			return 0;
		}
		public static IEnumerable<TResult> Zip<TFirst, TSecond, TResult>(this IEnumerable<TFirst> first, IEnumerable<TSecond> second, Func<TFirst, TSecond, TResult> resultSelector)
		{
			var a = first.GetEnumerator();
			var b = second.GetEnumerator();
			while (a.MoveNext() && b.MoveNext())
			{
				yield return resultSelector(a.Current, b.Current);
			}
		}
		
		public static void Compute(TextReader reader, TextWriter writer)
		{
//			var n = reader.ReadLine();
			reader.ReadLine();
			var xx = SplitToDoubles(reader.ReadLine());
			var yy = SplitToDoubles(reader.ReadLine());
			var xy = xx.Zip(yy, (x, y) => Math.Abs(x - y)).ToArray();
			
			var D1 = xy.Aggregate((total, next) => total += next);
			var D2 = Math.Sqrt(xy.Aggregate((total, next) => total += next * next));
			var D3 = Math.Pow(xy.Aggregate((total, next) => total += next * next * next), 1d / 3d);
			var D4 = xy.Max();
			
			writer.WriteLine(D1);
			writer.WriteLine(D2);
			writer.WriteLine(D3);
			writer.WriteLine(D4);
			
		}
	}
}