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 PHP (judge verdict: Accepted)

<?php
fscanf(STDIN, "%d", $n);

$format = join(' ', array_map(function ($x) { return '%f'; }, range(1, $n)));
$X = fscanf(STDIN, $format);
$Y = fscanf(STDIN, $format);

$dxy1 = pow(array_sum(array_map(func(1), $X, $Y)), 1);
$dxy2 = pow(array_sum(array_map(func(2), $X, $Y)), 1/2);
$dxy3 = pow(array_sum(array_map(func(3), $X, $Y)), 1/3);
$dxy4 = chebyshev_d($X, $Y);

echo "$dxy1\n";
echo "$dxy2\n";
echo "$dxy3\n";
echo "$dxy4\n";

function func($p)
{
    return function ($x, $y) use ($p) { return pow(abs($x - $y), $p); };
}

function chebyshev_d($X, $Y)
{
    $nums = array_map(function ($x, $y) { return abs($x - $y); }, $X, $Y);

    if (1 === count($nums)) {
        return $nums[0];
    }

    return call_user_func_array('max', $nums);
}