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.

Constraints

* $1 \leq n \leq 100$
* $0 \leq x_i, y_i \leq 1000$

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.

Example

Input

3
1 2 3
2 0 4


Output

4.000000
2.449490
2.154435
2.000000
#include <bits/stdc++.h>

using namespace std;

int main() {
	int n;
	cin >> n;
	vector<int64_t> x(n);
	for (auto &xi: x) {
		cin >> xi;
	}
	vector<int64_t> y(n);
	for (auto &yi: y) {
		cin >> yi;
	}
	int64_t sum1, sum2, sum3, best;
	sum1 = sum2 = sum3 = best = 0;
	for (auto i = 0; i < n; ++i) {
		auto diff = abs(x[i] - y[i]);
		sum1 += diff;
		sum2 += diff*diff;
		sum3 += diff*diff*diff;
		best = max(best, diff);
	}
	cout << fixed << setprecision(17);
	cout << sum1 << '\n' << sqrt(sum2) << '\n' << cbrt(sum3) << '\n' << best << '\n';
}
