"""simple docstring"""



from collections import defaultdict
class 						__UpperCAmelCase    :







			'''simple docstring'''





			def __init__(			self   ,      snake_case_   ,      snake_case_							):







										'''simple docstring'''


										A__       :     Tuple								=			total  # total no of tasks (N)

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

										A__       :     Optional[int]								=			defaultdict(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
										A__       :     Optional[int]								=			(1 << len(snake_case_							)) - 1





			def 		lowerCamelCase					(			self   ,      snake_case_   ,      snake_case_							):







										'''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
										A__       :     Optional[int]								=			self.count_ways_until(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.
										A__       :     List[str]								=			total_ways_util

										return self.dp[mask][task_no]





			def 		lowerCamelCase					(			self   ,      snake_case_							):







										'''simple docstring'''


										for i in range(len(snake_case_							)							):
																	for j in task_performed[i]:
																								self.task[j].append(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__":
				_UpperCamelCase								=		5  # total no of tasks (the value of N)

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






"""simple docstring"""



from __future__ import annotations

def  _A(		lowerCAmelCase							):
							if len(lowerCAmelCase							) == 0:
														return []
							A__				,							A__       :     Dict								=			min(lowerCAmelCase							), max(lowerCAmelCase							)
							A__       :     List[Any]								=			int(max_value - min_value							) + 1
							A__       :     list[list]								=			[[] for _ in range(lowerCAmelCase							)]

							for i in my_list:
														buckets[int(i - min_value							)].append(lowerCAmelCase							)

							return [v for bucket in buckets for v in sorted(lowerCAmelCase							)]


if __name__ == "__main__":
				from doctest import testmod

				testmod()
				assert bucket_sort([4, 5, 3, 2, 1]) == [1, 2, 3, 4, 5]
				assert bucket_sort([0, 1, -10, 15, 2, -2]) == [-10, -2, 0, 1, 2, 15]





