



from random import randint, random






def  UpperCAmelCase__    (    lowercase__						,       lowercase__						,       lowercase__						,       lowercase__ = False						,       lowercase__ = False						,       lowercase__ = 5						,       ) ->      list:
						__lowercase					=				[[-1] * number_of_cells]  # Create a highway without any car
						__lowercase					=				0
						__lowercase					=				max(lowercase__						,       0   )
						while i < number_of_cells:
												__lowercase					=				(
												    randint(0						,       lowercase__   ) if random_speed else initial_speed
												)  # Place the cars
												i += (
												    randint(1						,       max_speed * 2   ) if random_frequency else frequency
												)  # Arbitrary number, may need tuning
						return highway






def  UpperCAmelCase__    (    lowercase__						,       lowercase__   ) ->      int:
						__lowercase					=				0
						__lowercase					=				highway_now[car_index + 1 :]
						for cell in range(len(lowercase__   )   ):  # May need a better name for this
												if cells[cell] != -1:  # If the cell is not empty then
																		return distance  # we have the distance we wanted
												distance += 1
						# Here if the car is near the end of the highway
						return distance + get_distance(lowercase__						,       -1   )






def  UpperCAmelCase__    (    lowercase__						,       lowercase__						,       lowercase__   ) ->      list:
						__lowercase					=				len(lowercase__   )
						# Beforce calculations, the highway is empty
						__lowercase					=				[-1] * number_of_cells

						for car_index in range(lowercase__   ):
												if highway_now[car_index] != -1:
																		# Add 1 to the current speed of the car and cap the speed
																		__lowercase					=				min(highway_now[car_index] + 1						,       lowercase__   )
																		# Number of empty cell before the next car
																		__lowercase					=				get_distance(lowercase__						,       lowercase__   ) - 1
																		# We can't have the car causing an accident
																		__lowercase					=				min(next_highway[car_index]						,       lowercase__   )
																		if random() < probability:
																								# Randomly, a driver will slow down
																								__lowercase					=				max(next_highway[car_index] - 1						,       0   )
						return next_highway






def  UpperCAmelCase__    (    lowercase__						,       lowercase__						,       lowercase__						,       lowercase__   ) ->      list:
						__lowercase					=				len(highway[0]   )

						for i in range(lowercase__   ):
												__lowercase					=				update(highway[i]						,       lowercase__						,       lowercase__   )
												__lowercase					=				[-1] * number_of_cells

												for car_index in range(lowercase__   ):
																		__lowercase					=				next_speeds_calculated[car_index]
																		if speed != -1:
																								# Change the position based on the speed (with % to create the loop)
																								__lowercase					=				(car_index + speed) % number_of_cells
																								# Commit the change of position
																								__lowercase					=				speed
												highway.append(lowercase__   )

						return highway


if __name__ == "__main__":
			import doctest

			doctest.testmod()










def  UpperCAmelCase__    (    lowercase__ = 100   ) ->      int:
						__lowercase					=				n * (n + 1) * (2 * n + 1) / 6
						__lowercase					=				(n * (n + 1) / 2) ** 2
						return int(square_of_sum - sum_of_squares   )


if __name__ == "__main__":
			print(F"""{solution() = }""")





