


"""simple docstring"""
def 		lowercase							(     _snake_case						:      int     )     ->int:
	"""simple docstring"""





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

	__snake_case	:						List[Any]						=				[1]
	__snake_case	:						Optional[int]						=				(0, 0, 0)
	__snake_case	:						Tuple						=				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__":
			SCREAMING_SNAKE_CASE :    List[str]									=				input("""Enter the last number (nth term) of the Hamming Number Series: """)
			print("""Formula of Hamming Number Series => 2^i * 3^j * 5^k""")
			SCREAMING_SNAKE_CASE :    List[str]									=				hamming(int(n))
			print("""-----------------------------------------------------""")
			print(F'The list with nth numbers is: {hamming_numbers}')
			print("""-----------------------------------------------------""")







'''simple docstring'''







def 					UpperCAmelCase_		(__a      :    list ,	__a      :    list ,	__a      :    int ):






   """simple docstring"""

   _a				:	Optional[Any]			=   len(__a )
   _a				:	int			=   [[0] * n for i in range(__a )]
   for i in range(__a ):
      _a				:	Tuple			=   y_points[i]

   for i in range(2 ,	__a ):
      for j in range(__a ,	__a ):
         _a				:	Tuple			=   (
             (xa - x_points[j - i + 1]) * q[j][i - 1]
             - (xa - x_points[j]) * q[j - 1][i - 1]
         ) / (x_points[j] - x_points[j - i + 1])

   return [q[n - 1][n - 1], q]


if __name__ == "__main__":
  import doctest

  doctest.testmod()



