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);
$line = trim(fgets(STDIN));
$x = explode(' ', $line);
$line = trim(fgets(STDIN));
$y = explode(' ', $line);
$p = range(1, 4);

for ($i = 0; $i < 4; $i++) {
    $result = 0;
    foreach ($x as $j => $n) {
        $m = $y[$j];
        switch ($i) {
            case 0:
                $result += abs($n - $m);
                break;
            case 3:
                $result = max($result, abs($n - $m));
                break;
            default:
                $result += pow(abs($n - $m), $i + 1);
                break;
        }
    }

    if ($i === 1 || $i === 2) {
        $result = pow($result, 1 / ($i + 1));
    }

    printf("%f\n", $result);
}