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: Wrong Answer)

#!/usr/bin/env ruby

def manhattan(n, x_v, y_v)
  d = 0.0
  for i in 0..n.to_i-1 do
    d += (x_v[i].to_f - y_v[i].to_f).abs
  end
  d
end

def euc_i(n, x_v, y_v, p)
  d = 0.0
  for i in 0..n.to_i-1 do
    d += (x_v[i].to_f - y_v[i].to_f).abs ** p
  end
  d = d ** (1/p.to_f)
end

def chebshef(n, x_v, y_v)
  d = 0.0
  for i in 0..n.to_i-1 do
    c = (x_v[i].to_f - y_v[i].to_f).abs
    d > c ? d : d = c
  end
  d
end

n = STDIN.gets
x = STDIN.gets
y = STDIN.gets

if n.to_i < 1 and n.to_i > 100
   exit
end

x_v = x.split
y_v = y.split

puts sprintf("%.6f", manhattan(n, x_v, y_v))
puts sprintf("%.6f", euc_i(n, x_v, y_v, 2))
puts sprintf("%.6f", euc_i(n, x_v, y_v, 3))
puts sprintf("%.6f", chebshef(n, x, y))