


'''simple docstring'''
from collections import defaultdict
class    lowercase	:

		"""simple docstring"""

		def __init__(		self    ,   UpperCamelCase_    ,   UpperCamelCase_							):

							'''simple docstring'''


							UpperCamelCase__   :List[Any]												= total  # total no of tasks (N)

							# DP table will have a dimension of (2^M)*N
							# initially all values are set to -1
							UpperCamelCase__   :Union[str, Any]												= [
							    [-1 for i in range(total + 1							)] for j in range(2 ** len(UpperCamelCase_							)							)
							]

							UpperCamelCase__   :str												= defaultdict(UpperCamelCase_							)  # 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
							UpperCamelCase__   :Optional[int]												= (1 << len(UpperCamelCase_							)) - 1




		def     lowerCAmelCase__				(		self    ,   UpperCamelCase_    ,   UpperCamelCase_							):

							'''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
							UpperCamelCase__   :str												= self.count_ways_until(UpperCamelCase_    ,   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.
							UpperCamelCase__   :Optional[int]												= total_ways_util

							return self.dp[mask][task_no]




		def     lowerCAmelCase__				(		self    ,   UpperCamelCase_							):

							'''simple docstring'''


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

        # 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__":
		__snake_case							      =     5  # total no of tasks (the value of N)

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





def 				lowerCAmelCase_	(     snake_case_     ):
      if number < 0:
            raise ValueError("""number must not be negative"""     )
      return number & (number - 1) == 0


if __name__ == "__main__":
  import doctest

  doctest.testmod()

