





from random import randint, random





def lowerCAmelCase__(__snake_case       ,__snake_case       ,__snake_case       ,__snake_case = False       ,__snake_case = False       ,__snake_case = 5       ,)				->      list:







	'''simple docstring'''







	lowerCamelCase__								=		[[-1] * number_of_cells]  # Create a highway without any car
	lowerCamelCase__								=		0
	lowerCamelCase__								=		max(__snake_case       ,0							)
	while i < number_of_cells:
		lowerCamelCase__								=		(
		    randint(0       ,__snake_case							) 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 lowerCAmelCase__(__snake_case       ,__snake_case							)				->      int:







	'''simple docstring'''







	lowerCamelCase__								=		0
	lowerCamelCase__								=		highway_now[car_index + 1 :]
	for cell in range(len(__snake_case							)							):  # 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(__snake_case       ,-1							)





def lowerCAmelCase__(__snake_case       ,__snake_case       ,__snake_case							)				->      list:







	'''simple docstring'''







	lowerCamelCase__								=		len(__snake_case							)
	# Beforce calculations, the highway is empty
	lowerCamelCase__								=		[-1] * number_of_cells

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





def lowerCAmelCase__(__snake_case       ,__snake_case       ,__snake_case       ,__snake_case							)				->      list:







	'''simple docstring'''







	lowerCamelCase__								=		len(highway[0]							)

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

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

	return highway


if __name__ == "__main__":
			import doctest

			doctest.testmod()










from __future__ import annotations

from random import random






class 					__A    :

			'''simple docstring'''







			def __init__(    self       ,  __lowerCAmelCase = None							):



				'''simple docstring'''







				lowerCamelCase__								=		value
				lowerCamelCase__								=		random()
				lowerCamelCase__								=		None
				lowerCamelCase__								=		None





			def __repr__(    self							):



				'''simple docstring'''







				from pprint import pformat

				if self.left is None and self.right is None:
					return F'\'{self.value}: {self.prior:.5}\''
				else:
					return pformat(
					    {F'{self.value}: {self.prior:.5}': (self.left, self.right)}       ,  indent=1							)





			def __str__(    self							):



				'''simple docstring'''







				lowerCamelCase__								=		str(self.value							) + ''' '''
				lowerCamelCase__								=		str(self.left or ''''''							)
				lowerCamelCase__								=		str(self.right or ''''''							)
				return value + left + right





def lowerCAmelCase__(__snake_case       ,__snake_case							)				->      tuple[Node | None, Node | None]:







	'''simple docstring'''







	if root is None:  # None tree is split into 2 Nones
		return None, None
	elif root.value is None:
		return None, None
	else:
		if value < root.value:
			lowerCamelCase__				,	lowerCamelCase__								=		split(root.left       ,__snake_case							)
			return left, root
		else:
			lowerCamelCase__				,	lowerCamelCase__								=		split(root.right       ,__snake_case							)
			return root, right





def lowerCAmelCase__(__snake_case       ,__snake_case							)				->      Node | None:







	'''simple docstring'''







	if (not left) or (not right):  # If one node is None, return the other
		return left or right
	elif left.prior < right.prior:
		lowerCamelCase__								=		merge(left.right       ,__snake_case							)
		return left
	else:
		lowerCamelCase__								=		merge(__snake_case       ,right.left							)
		return right





def lowerCAmelCase__(__snake_case       ,__snake_case							)				->      Node | None:







	'''simple docstring'''







	lowerCamelCase__								=		Node(__snake_case							)
	lowerCamelCase__				,	lowerCamelCase__								=		split(__snake_case       ,__snake_case							)
	return merge(merge(__snake_case       ,__snake_case							)       ,__snake_case							)





def lowerCAmelCase__(__snake_case       ,__snake_case							)				->      Node | None:







	'''simple docstring'''







	lowerCamelCase__				,	lowerCamelCase__								=		split(__snake_case       ,value - 1							)
	lowerCamelCase__				,	lowerCamelCase__								=		split(__snake_case       ,__snake_case							)
	return merge(__snake_case       ,__snake_case							)





def lowerCAmelCase__(__snake_case							)				->      None:







	'''simple docstring'''







	if not root:  # None
		return
	else:
		inorder(root.left							)
		print(root.value       ,end=''','''							)
		inorder(root.right							)





def lowerCAmelCase__(__snake_case       ,__snake_case							)				->      Node | None:







	'''simple docstring'''







	for arg in args.split():
		if arg[0] == "+":
			lowerCamelCase__								=		insert(__snake_case       ,int(arg[1:]							)							)

		elif arg[0] == "-":
			lowerCamelCase__								=		erase(__snake_case       ,int(arg[1:]							)							)

		else:
			print('''Unknown command'''							)

	return root





def lowerCAmelCase__()				->      None:







	'''simple docstring'''







	lowerCamelCase__								=		None
	print(
	    '''enter numbers to create a tree, + value to add value into treap, '''
	    '''- value to erase all nodes with value. \'q\' to quit. '''							)

	lowerCamelCase__								=		input()
	while args != "q":
		lowerCamelCase__								=		interact_treap(__snake_case       ,__snake_case							)
		print(__snake_case							)
		lowerCamelCase__								=		input()

	print('''good by!'''							)


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			main()



