






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







def      snake_case		(							UpperCAmelCase	:       Optional[int]   ):



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


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					lowerCAmelCase_           = [
					    [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 manim import *
class      UpperCamelCase (				snake_case__ ):







		"""simple docstring"""



		def       A(  self		:       Dict		)    ->   Tuple:


						'''simple docstring'''
						A	 =      Rectangle(height=0.5						,width=0.5		)
						A	 =      Rectangle(height=0.46						,width=0.46		).set_stroke(width=0		)

						A	 =      [mem.copy() for i in range(6		)]
						A	 =      [mem.copy() for i in range(6		)]
						A	 =      VGroup(*_SCREAMING_SNAKE_CASE		).arrange(_SCREAMING_SNAKE_CASE						,buff=0		)
						A	 =      VGroup(*_SCREAMING_SNAKE_CASE		).arrange(_SCREAMING_SNAKE_CASE						,buff=0		)
						A	 =      VGroup(_SCREAMING_SNAKE_CASE						,_SCREAMING_SNAKE_CASE		).arrange(_SCREAMING_SNAKE_CASE						,buff=0		)
						A	 =      Text('CPU'						,font_size=2_4		)
						A	 =      Group(_SCREAMING_SNAKE_CASE						,_SCREAMING_SNAKE_CASE		).arrange(_SCREAMING_SNAKE_CASE						,buff=0.5						,aligned_edge=_SCREAMING_SNAKE_CASE		)
						cpu.move_to([-2.5, -0.5, 0]		)
						self.add(_SCREAMING_SNAKE_CASE		)

						A	 =      [mem.copy() for i in range(1		)]
						A	 =      VGroup(*_SCREAMING_SNAKE_CASE		).arrange(_SCREAMING_SNAKE_CASE						,buff=0		)
						A	 =      Text('GPU'						,font_size=2_4		)
						A	 =      Group(_SCREAMING_SNAKE_CASE						,_SCREAMING_SNAKE_CASE		).arrange(_SCREAMING_SNAKE_CASE						,buff=0.5						,aligned_edge=_SCREAMING_SNAKE_CASE		)
						gpu.align_to(_SCREAMING_SNAKE_CASE						,_SCREAMING_SNAKE_CASE		)
						gpu.set_x(gpu.get_x() - 1		)

						self.add(_SCREAMING_SNAKE_CASE		)

						A	 =      [mem.copy() for i in range(6		)]
						A	 =      VGroup(*_SCREAMING_SNAKE_CASE		).arrange(_SCREAMING_SNAKE_CASE						,buff=0		)

						A	 =      Text('Model'						,font_size=2_4		)
						A	 =      Group(_SCREAMING_SNAKE_CASE						,_SCREAMING_SNAKE_CASE		).arrange(_SCREAMING_SNAKE_CASE						,buff=0.5						,aligned_edge=_SCREAMING_SNAKE_CASE		)
						model.move_to([3, -1.0, 0]		)

						self.play(
						    Create(_SCREAMING_SNAKE_CASE						,run_time=1		)						,Create(_SCREAMING_SNAKE_CASE						,run_time=1		)						,Create(_SCREAMING_SNAKE_CASE						,run_time=1		)						,)

						A	 =      MarkupText(
						    f'First, an empty model skeleton is loaded\ninto <span fgcolor=\'{YELLOW}\'>memory</span> without using much RAM.'						,font_size=2_4						,)

						A	 =      Square(side_length=2.2		)
						key.move_to([-5, 2, 0]		)

						A	 =      MarkupText(
						    f'<b>Key:</b>\n\n<span fgcolor=\'{YELLOW}\'>●</span> Empty Model'						,font_size=1_8						,)

						key_text.move_to([-5, 2.4, 0]		)

						step_a.move_to([2, 2, 0]		)
						self.play(Write(_SCREAMING_SNAKE_CASE						,run_time=2.5		)						,Write(_SCREAMING_SNAKE_CASE		)						,Write(_SCREAMING_SNAKE_CASE		)		)

						self.add(_SCREAMING_SNAKE_CASE		)

						A	 =      []
						A	 =      []
						A	 =      []
						for i, rect in enumerate(_SCREAMING_SNAKE_CASE		):
										A	 =      Rectangle(height=0.46						,width=0.46		).set_stroke(width=0.0		).set_fill(_SCREAMING_SNAKE_CASE						,opacity=0.7		)
										cpu_target.move_to(_SCREAMING_SNAKE_CASE		)
										cpu_target.generate_target()
										A	 =      0.46 / 4
										A	 =      0.46 / 3

										if i == 0:
														cpu_target.target.next_to(cpu_left_col_base[0].get_corner(DOWN + LEFT		)						,buff=0.02						,direction=_SCREAMING_SNAKE_CASE		)
														cpu_target.target.set_x(cpu_target.target.get_x() + 0.1		)
										elif i == 3:
														cpu_target.target.next_to(cpu_targs[0].target						,direction=_SCREAMING_SNAKE_CASE						,buff=0.0		)
										else:
														cpu_target.target.next_to(cpu_targs[i - 1].target						,direction=_SCREAMING_SNAKE_CASE						,buff=0.0		)
										cpu_targs.append(_SCREAMING_SNAKE_CASE		)

										first_animations.append(rect.animate(run_time=0.5		).set_stroke(_SCREAMING_SNAKE_CASE		)		)
										second_animations.append(MoveToTarget(_SCREAMING_SNAKE_CASE						,run_time=1.5		)		)

						self.play(*_SCREAMING_SNAKE_CASE		)
						self.play(*_SCREAMING_SNAKE_CASE		)

						self.wait()





