



"""simple docstring"""







from __future__ import annotations

A		=						[True] * 1_0_0_0_0_0_1
A		=						2
while i * i <= 1_0_0_0_0_0_0:
			if seive[i]:
						for j in range(i * i, 1_0_0_0_0_0_1, i):
									A		=						False
			i += 1

def  __SCREAMING_SNAKE_CASE		(			lowerCamelCase_:							int ):
						"""simple docstring"""






						return seive[n]

def  __SCREAMING_SNAKE_CASE		(			lowerCamelCase_:							int ):
						"""simple docstring"""






						return any(digit in "02468" for digit in str(lowerCamelCase_ ) )

def  __SCREAMING_SNAKE_CASE		(			lowerCamelCase_:							int = 1_0_0_0_0_0_0 ):
						"""simple docstring"""






						snake_case   :			Optional[Any]						    = [2]  # result already includes the number 2.
						for num in range(3     ,		limit + 1     ,		2 ):
												if is_prime(lowerCamelCase_ ) and not contains_an_even_digit(lowerCamelCase_ ):
																		snake_case   :			Union[str, Any]						    = str(lowerCamelCase_ )
																		snake_case   :			int						    = [int(str_num[j:] + str_num[:j] ) for j in range(len(lowerCamelCase_ ) )]
																		if all(is_prime(lowerCamelCase_ ) for i in list_nums ):
																								result.append(lowerCamelCase_ )
						return result

def  __SCREAMING_SNAKE_CASE		(			):
						"""simple docstring"""






						return len(find_circular_primes() )


if __name__ == "__main__":
			print(F'''{len(find_circular_primes()) = }''')








"""simple docstring"""







from random import randint, random

def  __SCREAMING_SNAKE_CASE		(			lowerCamelCase_:							int     ,		lowerCamelCase_:							int     ,		lowerCamelCase_:							int     ,		lowerCamelCase_:							bool = False     ,		lowerCamelCase_:							bool = False     ,		lowerCamelCase_:							int = 5     ,		):
						"""simple docstring"""






						snake_case   :			str						    = [[-1] * number_of_cells]  # Create a highway without any car
						snake_case   :			str						    = 0
						snake_case   :			Any						    = max(lowerCamelCase_     ,		0 )
						while i < number_of_cells:
												snake_case   :			Optional[int]						    = (
												    randint(0     ,		lowerCamelCase_ ) 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  __SCREAMING_SNAKE_CASE		(			lowerCamelCase_:							list     ,		lowerCamelCase_:							int ):
						"""simple docstring"""






						snake_case   :			Any						    = 0
						snake_case   :			int						    = highway_now[car_index + 1 :]
						for cell in range(len(lowerCamelCase_ ) ):  # 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(lowerCamelCase_     ,		-1 )

def  __SCREAMING_SNAKE_CASE		(			lowerCamelCase_:							list     ,		lowerCamelCase_:							float     ,		lowerCamelCase_:							int ):
						"""simple docstring"""






						snake_case   :			List[str]						    = len(lowerCamelCase_ )
						# Beforce calculations, the highway is empty
						snake_case   :			Dict						    = [-1] * number_of_cells

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

def  __SCREAMING_SNAKE_CASE		(			lowerCamelCase_:							list     ,		lowerCamelCase_:							int     ,		lowerCamelCase_:							float     ,		lowerCamelCase_:							int ):
						"""simple docstring"""






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

						for i in range(lowerCamelCase_ ):
												snake_case   :			Union[str, Any]						    = update(highway[i]     ,		lowerCamelCase_     ,		lowerCamelCase_ )
												snake_case   :			Optional[int]						    = [-1] * number_of_cells

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

						return highway


if __name__ == "__main__":
			import doctest

			doctest.testmod()



