

'''simple docstring'''





def 							_lowerCAmelCase (      __magic_name__	:    int	)							->     list:
						lowercase   :       Optional[int]								=int(__magic_name__	)
						if n_element < 1:
												lowercase   :       Dict								=ValueError('''a should be a positive number'''	)
												raise my_error

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








'''simple docstring'''





from __future__ import annotations






def 							_lowerCAmelCase (      __magic_name__	:    list[list[int]]	)							->     bool:
						lowercase   :       str								=len(__magic_name__	)
						# We need to create solution object to save path.
						lowercase   :       int								=[[0 for _ in range(__magic_name__	)] for _ in range(__magic_name__	)]
						lowercase   :       List[Any]								=run_maze(__magic_name__      ,   0      ,   0      ,   __magic_name__	)
						if solved:
												print('''\n'''.join(str(__magic_name__	) for row in solutions	)	)
						else:
												print('''No solution exists!'''	)
						return solved






def 							_lowerCAmelCase (      __magic_name__	:    list[list[int]]      ,   __magic_name__	:    int      ,   __magic_name__	:    int      ,   __magic_name__	:    list[list[int]]	)							->     bool:
						lowercase   :       Optional[int]								=len(__magic_name__	)
						# Final check point.
						if i == j == (size - 1):
												lowercase   :       Optional[int]								=1
												return True

						lowercase   :       Optional[int]								=(not i < 0) and (not j < 0)  # Check lower bounds
						lowercase   :       Tuple								=(i < size) and (j < size)  # Check upper bounds

						if lower_flag and upper_flag:
												# check for already visited and block points.
												lowercase   :       Union[str, Any]								=(not solutions[i][j]) and (not maze[i][j])
												if block_flag:
																		# check visited
																		lowercase   :       Union[str, Any]								=1

																		# check for directions
																		if (
																		    run_maze(__magic_name__      ,   i + 1      ,   __magic_name__      ,   __magic_name__	)
																		    or run_maze(__magic_name__      ,   __magic_name__      ,   j + 1      ,   __magic_name__	)
																		    or run_maze(__magic_name__      ,   i - 1      ,   __magic_name__      ,   __magic_name__	)
																		    or run_maze(__magic_name__      ,   __magic_name__      ,   j - 1      ,   __magic_name__	)
																		):
																								return True

																		lowercase   :       str								=0
																		return False
						return False


if __name__ == "__main__":
							import doctest

							doctest.testmod()





