


from collections import defaultdict






class     UpperCamelCase:


					def __init__(						self	:		Optional[int]     ,    SCREAMING_SNAKE_CASE	:		Optional[int]     ,    SCREAMING_SNAKE_CASE	:		Tuple						)			->	Optional[int]:




											'''simple docstring'''

											__snake_case				=		total  # total no of tasks (N)

											# DP table will have a dimension of (2^M)*N
											# initially all values are set to -1
											__snake_case				=		[
											    [-1 for i in range(total + 1						)] for j in range(2 ** len(SCREAMING_SNAKE_CASE						)						)
											]

											__snake_case				=		defaultdict(SCREAMING_SNAKE_CASE						)  # stores the list of persons for each task

											# final_mask is used to check if all persons are included by setting all bits
											# to 1
											__snake_case				=		(1 << len(SCREAMING_SNAKE_CASE						)) - 1


					def 							SCREAMING_SNAKE_CASE_  (						self	:		Dict     ,    SCREAMING_SNAKE_CASE	:		Union[str, Any]     ,    SCREAMING_SNAKE_CASE	:		List[str]						)			->	Optional[Any]:




											'''simple docstring'''

											if mask == self.final_mask:
																	return 1

											# if not everyone gets the task and no more tasks are available, return 0
											if task_no > self.total_tasks:
																	return 0

											# if case already considered
											if self.dp[mask][task_no] != -1:
																	return self.dp[mask][task_no]

											# Number of ways when we don't this task in the arrangement
											__snake_case				=		self.count_ways_until(SCREAMING_SNAKE_CASE     ,    task_no + 1						)

											# now assign the tasks one by one to all possible persons and recursively
											# assign for the remaining tasks.
											if task_no in self.task:
																	for p in self.task[task_no]:
																							# if p is already given a task
																							if mask & (1 << p):
																													continue

																							# assign this task to p and change the mask value. And recursively
																							# assign tasks with the new mask value.
																							total_ways_util += self.count_ways_until(mask | (1 << p)     ,    task_no + 1						)

        # save the value.
											__snake_case				=		total_ways_util

											return self.dp[mask][task_no]






					def 							SCREAMING_SNAKE_CASE_  (						self	:		Dict     ,    SCREAMING_SNAKE_CASE	:		int						)			->	Union[str, Any]:




											'''simple docstring'''

											for i in range(len(SCREAMING_SNAKE_CASE						)						):
																	for j in task_performed[i]:
																							self.task[j].append(SCREAMING_SNAKE_CASE						)

        # call the function to fill the DP table, final answer is stored in dp[0][1]
											return self.count_ways_until(0     ,    1						)


if __name__ == "__main__":
						A							:					Optional[Any]     						=     5  # total no of tasks (the value of N)

						# the list of tasks that can be done by M persons.
						A							:					str     						=     [[1, 3, 4], [1, 2, 5], [3, 4]]
						print(
						    AssignmentUsingBitmask(task_performed, total_tasks).count_no_of_ways(
						        task_performed
						    )
						)









from __future__ import annotations

from decimal import Decimal
from math import *  # noqa: F403

from sympy import diff





def 	_lowerCAmelCase       (    _lowerCAmelCase      ,	_lowerCAmelCase      ,	_lowerCAmelCase = 10**-10 )						->	float:


						'''simple docstring'''






						__snake_case				=		a
						while True:
												__snake_case				=		Decimal(_lowerCAmelCase ) - (
												    Decimal(eval(_lowerCAmelCase ) ) / Decimal(eval(str(diff(_lowerCAmelCase ) ) ) )  # noqa: S307
												)
												# This number dictates the accuracy of the answer
												if abs(eval(_lowerCAmelCase ) ) < precision:  # noqa: S307
																		return float(_lowerCAmelCase )


# Let's Execute
if __name__ == "__main__":
	# Find root of trigonometric function
	# Find value of pi
	print(f'''The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}''')
	# Find root of polynomial
	print(f'''The root of x**2 - 5*x + 2 = 0 is {newton_raphson("x**2 - 5*x + 2", 0.4)}''')
	# Find Square Root of 5
	print(f'''The root of log(x) - 1 = 0 is {newton_raphson("log(x) - 1", 2)}''')
	# Exponential Roots
	print(f'''The root of exp(x) - 1 = 0 is {newton_raphson("exp(x) - 1", 0)}''')





