






"""simple docstring"""


import math
from decimal import Decimal, getcontext


def 					UpperCAmelCase			(				a__ = 4_00_00_00   ):





						'''simple docstring'''






						try:
												lowerCAmelCase      :Optional[int]				  = int(a__   )
						except (TypeError, ValueError):
												raise TypeError('Parameter n must be int or castable to int.'   )
						if n <= 0:
												raise ValueError('Parameter n must be greater than or equal to one.'   )
						lowerCAmelCase      :Tuple				  = 1_00
						lowerCAmelCase      :List[str]				  = (Decimal(5   ) ** Decimal(0.5   ) + 1) / Decimal(2   )

						lowerCAmelCase      :int				  = (math.floor(math.log(n * (phi + 2)    ,			a__   ) - 1   ) // 3) * 3 + 2
						lowerCAmelCase      :List[str]				  = Decimal(round(phi ** Decimal(index + 1   )   )   ) / (phi + 2)
						lowerCAmelCase      :Tuple				  = num // 2
						return int(a__   )


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







"""simple docstring"""


from __future__ import annotations


def 					UpperCAmelCase			(				a__   ):





						'''simple docstring'''






						lowerCAmelCase      :Union[str, Any]				  = [0] * len(a__   )
						for i in range(1    ,			len(a__   )   ):
												lowerCAmelCase      :Optional[int]				  = duration_times[i - 1] + waiting_times[i - 1]
						return waiting_times


def 					UpperCAmelCase			(				a__    ,			a__   ):





						'''simple docstring'''






						return [
						    duration_time + waiting_times[i]
						    for i, duration_time in enumerate(a__   )
						]


def 					UpperCAmelCase			(				a__   ):





						'''simple docstring'''






						return sum(a__   ) / len(a__   )


def 					UpperCAmelCase			(				a__   ):





						'''simple docstring'''






						return sum(a__   ) / len(a__   )


if __name__ == "__main__":
		# process id's
		__SCREAMING_SNAKE_CASE      =      [1, 2, 3]

		# ensure that we actually have processes
		if len(processes) == 0:
				print('Zero amount of processes')
				raise SystemExit(0)

		# duration time of all processes
		__SCREAMING_SNAKE_CASE      =      [19, 8, 9]

		# ensure we can match each id to a duration time
		if len(duration_times) != len(processes):
				print('Unable to match all id\'s with their duration time')
				raise SystemExit(0)

		# get the waiting times and the turnaround times
		__SCREAMING_SNAKE_CASE      =      calculate_waiting_times(duration_times)
		__SCREAMING_SNAKE_CASE      =      calculate_turnaround_times(duration_times, waiting_times)

		# get the average times
		__SCREAMING_SNAKE_CASE      =      calculate_average_waiting_time(waiting_times)
		__SCREAMING_SNAKE_CASE      =      calculate_average_turnaround_time(turnaround_times)

		# print all the results
		print('Process ID\tDuration Time\tWaiting Time\tTurnaround Time')
		for i, process in enumerate(processes):
				print(
				    F"""{process}\t\t{duration_times[i]}\t\t{waiting_times[i]}\t\t"""
				    F"""{turnaround_times[i]}"""
				)
		print(F"""Average waiting time = {average_waiting_time}""")
		print(F"""Average turn around time = {average_turnaround_time}""")