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 JavaScript (judge verdict: Accepted)

//config = {stdin: 'tmp', newline: '\r\n'}; // win
config = {stdin: '/dev/stdin', newline: '\n'}; // linux

line = require('fs').readFileSync(config.stdin, 'ascii')
       .split(config.newline, 3)
       .map(function(line) {
         return line.split(' ').map(Number);
       });

dist = (function (x, y) {
  var res = [];
  for (var i in x) res.push(Math.abs(x[i] - y[i]));
  return res;
}) (line[1], line[2]);

console.log(
  dist.reduce(function (prev, cur) { return prev + cur; }, 0));
console.log(
  Math.sqrt(
    dist.reduce(function (prev, cur) { return prev + cur * cur; }, 0)));
console.log(
  Math.pow(
    dist.reduce(function (prev, cur) { return prev + cur * cur * cur; }, 0),
    1/3));
console.log(
  dist.reduce(function (prev, cur) { return Math.max(prev, cur); }, 0));