



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






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


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					snake_case_ :	Union[str, Any]         =  [
					    [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]]))



from multiprocessing import Lock, Pipe, Process

# lock used to ensure that two processes do not access a pipe at the same time
__a  :     List[str]       =  Lock()





def 				UpperCAmelCase						(    lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							):







				"""simple docstring"""



				global process_lock

				# we perform n swaps since after n swaps we know we are sorted
				# we *could* stop early if we are sorted already, but it takes as long to
				# find out we are sorted as it does to sort the list with this algorithm
				for i in range(0							,			10							):
								if (i + position) % 2 == 0 and r_send is not None:
												# send your value to your right neighbor
												process_lock.acquire()
												r_send[1].send(lowercase							)
												process_lock.release()

												# receive your right neighbor's value
												process_lock.acquire()
												__lowercase 			=							rr_cv[0].recv()
												process_lock.release()

												# take the lower value since you are on the left
												__lowercase 			=							min(lowercase							,			lowercase							)
								elif (i + position) % 2 != 0 and l_send is not None:
												# send your value to your left neighbor
												process_lock.acquire()
												l_send[1].send(lowercase							)
												process_lock.release()

												# receive your left neighbor's value
												process_lock.acquire()
												__lowercase 			=							lr_cv[0].recv()
												process_lock.release()

												# take the higher value since you are on the right
												__lowercase 			=							max(lowercase							,			lowercase							)
    # after all swaps are performed, send the values back to main
				result_pipe[1].send(lowercase							)





def 				UpperCAmelCase						(    lowercase							):







				"""simple docstring"""



				__lowercase 			=							[]
				__lowercase 			=							[]
				# initialize the list of pipes where the values will be retrieved
				for _ in arr:
								result_pipe.append(Pipe()							)
				# creates the processes
				# the first and last process only have one neighbor so they are made outside
				# of the loop
				__lowercase 			=							Pipe()
				__lowercase 			=							Pipe()
				process_array_.append(
				    Process(
				        target=lowercase							,			args=(0, arr[0], None, temp_rs, None, temp_rr, result_pipe[0])							,			)							)
				__lowercase 			=							temp_rs
				__lowercase 			=							temp_rr

				for i in range(1							,			len(lowercase							) - 1							):
								__lowercase 			=							Pipe()
								__lowercase 			=							Pipe()
								process_array_.append(
								    Process(
								        target=lowercase							,			args=(i, arr[i], temp_ls, temp_rs, temp_lr, temp_rr, result_pipe[i])							,			)							)
								__lowercase 			=							temp_rs
								__lowercase 			=							temp_rr

				process_array_.append(
				    Process(
				        target=lowercase							,			args=(
				            len(lowercase							) - 1,
				            arr[len(lowercase							) - 1],
				            temp_ls,
				            None,
				            temp_lr,
				            None,
				            result_pipe[len(lowercase							) - 1],
				        )							,			)							)

				# start the processes
				for p in process_array_:
								p.start()

				# wait for the processes to end and write their values to the list
				for p in range(0							,			len(lowercase							)							):
								__lowercase 			=							result_pipe[p][0].recv()
								process_array_[p].join()
				return arr





def 				UpperCAmelCase						(    ):







				"""simple docstring"""



				__lowercase 			=							list(range(10							,			0							,			-1							)							)
				print('''Initial List'''							)
				print(*lowercase							)
				__lowercase 			=							odd_even_transposition(lowercase							)
				print('''Sorted List\n'''							)
				print(*lowercase							)


if __name__ == "__main__":
		main()