





def     snake_case							(UpperCamelCase			:     Union[str, Any]			,    UpperCamelCase			:     str							):




	'''simple docstring'''







	_validate_point(UpperCamelCase							)
	_validate_point(UpperCamelCase							)
	if len(UpperCamelCase							) != len(UpperCamelCase							):
		raise ValueError("""Both points must be in the same n-dimensional space"""							)

	return float(sum(abs(a - b							) for a, b in zip(UpperCamelCase			,    UpperCamelCase							)							)							)

def     snake_case							(UpperCamelCase			:     Union[str, Any]							):




	'''simple docstring'''







	if point:
		if isinstance(UpperCamelCase			,    UpperCamelCase							):
			for item in point:
				if not isinstance(UpperCamelCase			,    (int, float)							):
					lowerCamelCase__										=			(
					    """Expected a list of numbers as input, found """
					    f'''{type(UpperCamelCase							).__name__}'''
					)
					raise TypeError(UpperCamelCase							)
		else:
			lowerCamelCase__										=			f'''Expected a list of numbers as input, found {type(UpperCamelCase							).__name__}'''
			raise TypeError(UpperCamelCase							)
	else:
		raise ValueError("""Missing an input"""							)

def     snake_case							(UpperCamelCase			:     Union[str, Any]			,    UpperCamelCase			:     str							):




	'''simple docstring'''







	_validate_point(UpperCamelCase							)
	_validate_point(UpperCamelCase							)
	if len(UpperCamelCase							) != len(UpperCamelCase							):
		raise ValueError("""Both points must be in the same n-dimensional space"""							)

	return float(sum(abs(x - y							) for x, y in zip(UpperCamelCase			,    UpperCamelCase							)							)							)


if __name__ == "__main__":
					import doctest

					doctest.testmod()






'''simple docstring'''


def 						lowerCamelCase__   (				a							):
						__snake_case						 =   int(a							)
						if n_element < 1:
												__snake_case						 =   ValueError('a should be a positive number'							)
												raise my_error

						__snake_case						 =   [1]
						__snake_case ,       __snake_case ,       __snake_case						 =   (0, 0, 0)
						__snake_case						 =   1
						while index < n_element:
												while hamming_list[i] * 2 <= hamming_list[-1]:
																		i += 1
												while hamming_list[j] * 3 <= hamming_list[-1]:
																		j += 1
												while hamming_list[k] * 5 <= hamming_list[-1]:
																		k += 1
												hamming_list.append(
												    min(hamming_list[i] * 2    ,	hamming_list[j] * 3    ,	hamming_list[k] * 5							)							)
												index += 1
						return hamming_list


if __name__ == "__main__":
	_lowercase  =			input("""Enter the last number (nth term) of the Hamming Number Series: """)
	print("""Formula of Hamming Number Series => 2^i * 3^j * 5^k""")
	_lowercase  =			hamming(int(n))
	print("""-----------------------------------------------------""")
	print(f'''The list with nth numbers is: {hamming_numbers}''')
	print("""-----------------------------------------------------""")

