






def   __lowercase       (			snake_case			):







				"""simple docstring"""






				__magic_name__		:str   =   current_set.copy()
				for row_index, row in enumerate(snake_case			):
								__magic_name__		:Tuple   =   row[0]
								for column_index, column in enumerate(snake_case			):
												if magnitude == 0:
																__magic_name__		:Optional[Any]   =   column
																continue
												__magic_name__		:Union[str, Any]   =   column / magnitude
    # Subtract to cancel term
				__magic_name__		:List[str]   =   current_set[0]
				__magic_name__		:List[Any]   =   [first_row]
				__magic_name__		:Any   =   current_set[1::]
				for row in current_set:
								__magic_name__		:str   =   []
								# If first term is 0, it is already in form we want, so we preserve it
								if row[0] == 0:
												final_set.append(snake_case			)
												continue
								for column_index in range(len(snake_case			)			):
												temp_row.append(first_row[column_index] - row[column_index]			)
								final_set.append(snake_case			)
				# Create next recursion iteration set
				if len(final_set[0]			) != 3:
								__magic_name__		:Tuple   =   final_set[0]
								__magic_name__		:List[Any]   =   []
								__magic_name__		:int   =   []
								for row in final_set[1::]:
												current_first_column.append(row[0]			)
												next_iteration.append(row[1::]			)
								__magic_name__		:int   =   simplify(snake_case			)
								for i in range(len(snake_case			)			):
												resultant[i].insert(0,	current_first_column[i]			)
								resultant.insert(0,	snake_case			)
								__magic_name__		:Any   =   resultant
				return final_set

def   __lowercase       (			snake_case			):







				"""simple docstring"""






				if len(snake_case			) == 0:
								raise IndexError('''solve_simultaneous() requires n lists of length n+1'''			)
				__magic_name__		:int   =   len(snake_case			) + 1
				if any(len(snake_case			) != _length for item in equations			):
								raise IndexError('''solve_simultaneous() requires n lists of length n+1'''			)
				for row in equations:
								if any(not isinstance(snake_case,	(int, float)			) for column in row			):
												raise ValueError('''solve_simultaneous() requires lists of integers'''			)
				if len(snake_case			) == 1:
								return [equations[0][-1] / equations[0][0]]
				__magic_name__		:List[Any]   =   equations.copy()
				if any(0 in row for row in data_set			):
								__magic_name__		:Any   =   data_set.copy()
								__magic_name__		:List[str]   =   []
								for row_index, row in enumerate(snake_case			):
												if 0 not in row:
																__magic_name__		:Any   =   data_set.pop(snake_case			)
																break
								if not full_row:
												raise ValueError('''solve_simultaneous() requires at least 1 full equation'''			)
								data_set.insert(0,	snake_case			)
				__magic_name__		:Tuple   =   data_set.copy()
				__magic_name__		:Optional[Any]   =   simplify(snake_case			)
				__magic_name__		:Optional[Any]   =   simplified[::-1]
				__magic_name__		:list   =   []
				for row in simplified:
								__magic_name__		:int   =   row[-1]
								if not solutions:
												if row[-2] == 0:
																solutions.append(0			)
																continue
												solutions.append(current_solution / row[-2]			)
												continue
								__magic_name__		:Union[str, Any]   =   row.copy()[: len(snake_case			) - 1 :]
								while temp_row[0] == 0:
												temp_row.pop(0			)
								if len(snake_case			) == 0:
												solutions.append(0			)
												continue
								__magic_name__		:Dict   =   temp_row[1::]
								__magic_name__		:Any   =   temp_row[::-1]
								for column_index, column in enumerate(snake_case			):
												current_solution -= column * solutions[column_index]
								solutions.append(snake_case			)
				__magic_name__		:List[Any]   =   []
				for item in solutions:
								final.append(float(round(snake_case,	5			)			)			)
				return final[::-1]


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					SCREAMING_SNAKE_CASE__   :      List[str]				=		[
					    [2, 1, 1, 1, 1, 4],
					    [1, 2, 1, 1, 1, 5],
					    [1, 1, 2, 1, 1, 6],
					    [1, 1, 1, 2, 1, 7],
					    [1, 1, 1, 1, 2, 8],
					]
					print(solve_simultaneous(eq))
					print(solve_simultaneous([[4, 2]]))














def   __lowercase       (			snake_case			):







				"""simple docstring"""






				if not isinstance(snake_case,	snake_case			):
								raise ValueError('''multiplicative_persistence() only accepts integral values'''			)
				if num < 0:
								raise ValueError('''multiplicative_persistence() does not accept negative values'''			)

				__magic_name__		:str   =   0
				__magic_name__		:Dict   =   str(snake_case			)

				while len(snake_case			) != 1:
								__magic_name__		:Optional[Any]   =   [int(snake_case			) for i in num_string]

								__magic_name__		:Dict   =   1
								for i in range(0,	len(snake_case			)			):
												total *= numbers[i]

								__magic_name__		:int   =   str(snake_case			)

								steps += 1
				return steps

def   __lowercase       (			snake_case			):







				"""simple docstring"""






				if not isinstance(snake_case,	snake_case			):
								raise ValueError('''additive_persistence() only accepts integral values'''			)
				if num < 0:
								raise ValueError('''additive_persistence() does not accept negative values'''			)

				__magic_name__		:str   =   0
				__magic_name__		:Union[str, Any]   =   str(snake_case			)

				while len(snake_case			) != 1:
								__magic_name__		:str   =   [int(snake_case			) for i in num_string]

								__magic_name__		:Optional[int]   =   0
								for i in range(0,	len(snake_case			)			):
												total += numbers[i]

								__magic_name__		:int   =   str(snake_case			)

								steps += 1
				return steps


if __name__ == "__main__":
					import doctest

					doctest.testmod()






