
from random import randint, random


def       A       (					lowercase    ,       lowercase    ,       lowercase    ,       lowercase = False    ,       lowercase = False    ,       lowercase = 5    ,       )   ->  list:
		'''simple docstring'''

		UpperCamelCase		=     [[-1] * number_of_cells]  # Create a highway without any car
		UpperCamelCase		=     0
		UpperCamelCase		=     max(lowercase    ,       0 )
		while i < number_of_cells:
				UpperCamelCase		=     (
				    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       A       (					lowercase    ,       lowercase )   ->  int:
		'''simple docstring'''

		UpperCamelCase		=     0
		UpperCamelCase		=     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       A       (					lowercase    ,       lowercase    ,       lowercase )   ->  list:
		'''simple docstring'''

		UpperCamelCase		=     len(lowercase )
		# Beforce calculations, the highway is empty
		UpperCamelCase		=     [-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
						UpperCamelCase		=     min(highway_now[car_index] + 1    ,       lowercase )
						# Number of empty cell before the next car
						UpperCamelCase		=     get_distance(lowercase    ,       lowercase ) - 1
						# We can't have the car causing an accident
						UpperCamelCase		=     min(next_highway[car_index]    ,       lowercase )
						if random() < probability:
								# Randomly, a driver will slow down
								UpperCamelCase		=     max(next_highway[car_index] - 1    ,       0 )
		return next_highway


def       A       (					lowercase    ,       lowercase    ,       lowercase    ,       lowercase )   ->  list:
		'''simple docstring'''

		UpperCamelCase		=     len(highway[0] )

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

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

		return highway


if __name__ == "__main__":
					import doctest

					doctest.testmod()


from decimal import Decimal, getcontext
from math import ceil, factorial


def       A       (					lowercase )   ->  str:
		'''simple docstring'''

		if not isinstance(lowercase    ,       lowercase ):
				raise TypeError('Undefined for non-integers' )
		elif precision < 1:
				raise ValueError('Undefined for non-natural numbers' )

		UpperCamelCase		=     precision
		UpperCamelCase		=     ceil(precision / 14 )
		UpperCamelCase		=     426_880 * Decimal(10_005 ).sqrt()
		UpperCamelCase		=     1
		UpperCamelCase		=     13_591_409
		UpperCamelCase		=     Decimal(lowercase )
		for k in range(1    ,       lowercase ):
				UpperCamelCase		=     factorial(6 * k ) // (factorial(3 * k ) * factorial(lowercase ) ** 3)
				linear_term += 545_140_134
				exponential_term *= -262_537_412_640_768_000
				partial_sum += Decimal(multinomial_term * linear_term ) / exponential_term
		return str(constant_term / partial_sum )[:-1]


if __name__ == "__main__":
					_UpperCAmelCase					: Dict      =       50
					print(F'''The first {n} digits of pi is: {pi(n)}''')
