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 Python3 (judge verdict: Wrong Answer)

# 22-Math_Functions-Distance_II.py

# ??????????????????????????¢
# ???????????????????????????????????????????????????????????????????????¢??§??¬???????????????
# ????????????????????°???????????????????§?????????¨????????§????????????????????????
# ????????§??????????????? n ?¬????????????????
#  x={x1,x2,...,xn} ??¨
#  y={y1,y2,...,yn} 
# ????????¢????¨????????????????????????????

# ????????????????????????????????¢?????¬???????¨?????????¨?????¨??????????¬??????????????????????????????¢?????\????????????????????? 
# Dxy=(???{i=1n}|xi???yi|^p)1/p

# p=1 ?????¨??? 
# Dxy=|x1???y1|+|x2???y2|+...+|xn???yn|

# ??¨?????????????????????????????????????????¢??¨?????°???????????? 

# p=2 ?????¨??? 
# Dxy=(|x1???y1|)2+(|x2???y2|)2+...+(|xn???yn|)2?????????????????????????????????????????????????????????????????????????????????????????????????????????
# ??¨???????????????????????¬?????????????????????????????????????????¢?????????????????? 

# p=??? ?????¨??? 
# Dxy=maxni=1(|xi???yi|)
# ??¨???????????????????????§????????§????????¢??¨?????°????????????

# ????????? n ?¬???????????????????????????????????????§???
# p ??????????????? 1???2???3?????? ?????????????????????????????¢????±???????????????°????????????????????????????????????

# Input
# ??????????????´??° n ????????????????????????
# ???????????????????????? x ???????´? {x1,x2,...xn}{x1,x2,...xn}???
# ???????????????????????? y ???????´? {y1,y2,...yn}{y1,y2,...yn} 
# ????????????????????§???????????????????????\?????????????????´??°?????§??????

# Output
# p ??????????????? 1???2???3?????? ??????????????????????????????????????¢??????????????????????????????
# ????????????0.00001 ??\????????????????????£????????????????????¨????????????

# Constraints
# 1???n???100
# 0???xi,yi???1000
# Sample Input
# 3
# 1 2 3
# 2 0 4
# Sample Output
# 4.000000
# 2.449490
# 2.154435
# 2.000000

n = int(input())
x = list( map(int, input().split()) )
y = list( map(int, input().split()) )
pp=[1,2,3,100]


for p in pp:
	print(  sum( [abs(x[i]-y[i])**p for i in range(n)] )**(1/p)  )