






'''simple docstring'''
from random import randint, random





def 	_a(					UpperCamelCase__			:  int,		UpperCamelCase__			:  int,		UpperCamelCase__			:  int,		UpperCamelCase__			:  bool = False,		UpperCamelCase__			:  bool = False,		UpperCamelCase__			:  int = 5,		):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__       :			Optional[Any]													=[[-1] * number_of_cells]  # Create a highway without any car
      SCREAMING_SNAKE_CASE__       :			Tuple													=0
      SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=max(UpperCamelCase__,		0							)
      while i < number_of_cells:
            SCREAMING_SNAKE_CASE__       :			Dict													=(
                randint(0,		UpperCamelCase__							) 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 	_a(					UpperCamelCase__			:  list,		UpperCamelCase__			:  int							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=0
      SCREAMING_SNAKE_CASE__       :			List[str]													=highway_now[car_index + 1 :]
      for cell in range(len(UpperCamelCase__							)							):  # 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(UpperCamelCase__,		-1							)





def 	_a(					UpperCamelCase__			:  list,		UpperCamelCase__			:  float,		UpperCamelCase__			:  int							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__       :			int													=len(UpperCamelCase__							)
      # Beforce calculations, the highway is empty
      SCREAMING_SNAKE_CASE__       :			List[str]													=[-1] * number_of_cells

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





def 	_a(					UpperCamelCase__			:  list,		UpperCamelCase__			:  int,		UpperCamelCase__			:  float,		UpperCamelCase__			:  int							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__       :			Optional[Any]													=len(highway[0]							)

      for i in range(UpperCamelCase__							):
            SCREAMING_SNAKE_CASE__       :			List[str]													=update(highway[i],		UpperCamelCase__,		UpperCamelCase__							)
            SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=[-1] * number_of_cells

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

      return highway


if __name__ == "__main__":
     import doctest

     doctest.testmod()







'''simple docstring'''
def 	_a(					UpperCamelCase__			:  Optional[Any]=2_8_1_2_3							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__       :			List[Any]													=[1] * (limit + 1)

      for i in range(2,		int(limit**0.5							) + 1							):
            sum_divs[i * i] += i
            for k in range(i + 1,		limit // i + 1							):
                  sum_divs[k * i] += k + i

      SCREAMING_SNAKE_CASE__       :			List[str]													=set()
      SCREAMING_SNAKE_CASE__       :			str													=0

      for n in range(1,		limit + 1							):
            if sum_divs[n] > n:
                  abundants.add(UpperCamelCase__							)

            if not any((n - a in abundants) for a in abundants							):
                  res += n

      return res


if __name__ == "__main__":
  print(solution())