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 Ruby (judge verdict: Accepted)

MODE = "stdio"
require 'matrix'
include Math
line = Array.new

if(defined? MODE)
  line = STDIN.read.split("\n")
else
  tmp = '3
  1 2 3
  2 0 4'.split("\n")
  tmp.each{|s|
    line << s.strip
  }
end
 n = line[0].to_i
 

x = line[1].split(" ").map(&:to_i)
y = line[2].split(" ").map(&:to_i)

xy = x.zip(y).map{|x,y| (x-y).abs.to_f}
p2 = xy.map{|xy| xy**2}.inject(&:+)
p3 = xy.map{|xy| xy**3}.inject(&:+)

p1 = xy.inject(&:+)
p2 = p2**(1.0/2)
p3 = p3**(1.0/3)
pinf = xy.max

printf("%.10f\n%.10f\n%.10f\n%.10f\n",p1,p2,p3,pinf)