
"""simple docstring"""





class     _UpperCAmelCase:



		def __init__(					self)       ->       Optional[Any]:






							'''simple docstring'''
							_UpperCamelCase							 =  {}



		def 						UpperCAmelCase							(					self)       ->       None:






							'''simple docstring'''
							print(self.vertex)
							for i in self.vertex:
												print(__a				,		''' -> '''				,		''' -> '''.join([str(__a) for j in self.vertex[i]]))



		def 						UpperCAmelCase							(					self				,		__a				,		__a)       ->       None:






							'''simple docstring'''
							# check if vertex is already present,
							if from_vertex in self.vertex:
												self.vertex[from_vertex].append(__a)
							else:
												# else make a new vertex
												_UpperCamelCase							 =  [to_vertex]



		def 						UpperCAmelCase							(					self)       ->       None:






							'''simple docstring'''
							# visited array for storing already visited nodes
							_UpperCamelCase							 =  [False] * len(self.vertex)

							# call the recursive helper function
							for i in range(len(self.vertex)):
												if not visited[i]:
																	self.dfs_recursive(__a				,		__a)




		def 						UpperCAmelCase							(					self				,		__a				,		__a)       ->       None:






							'''simple docstring'''
							# mark start vertex as visited
							_UpperCamelCase							 =  True

							print(__a				,		end=''' ''')

							# Recur for all the vertices that are adjacent to this node
							for i in self.vertex:
												if not visited[i]:
																	self.dfs_recursive(__a				,		__a)


if __name__ == "__main__":
				_a														=		Graph()
				g.add_edge(0, 1)
				g.add_edge(0, 2)
				g.add_edge(1, 2)
				g.add_edge(2, 0)
				g.add_edge(2, 3)
				g.add_edge(3, 3)

				g.print_graph()
				print("""DFS:""")
				g.dfs()

				# OUTPUT:
				# 0  ->  1 -> 2
				# 1  ->  2
				# 2  ->  0 -> 3
				# 3  ->  3
				# DFS:
				#  0 1 2 3








"""simple docstring"""





from collections import defaultdict






class     _UpperCAmelCase:



		def __init__(					self				,		__a				,		__a)       ->       Union[str, Any]:






							'''simple docstring'''
							_UpperCamelCase							 =  total  # total no of tasks (N)

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

							_UpperCamelCase							 =  defaultdict(__a)  # 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							 =  (1 << len(__a)) - 1



		def 						UpperCAmelCase							(					self				,		__a				,		__a)       ->       Dict:






							'''simple docstring'''
							# if mask == self.finalmask all persons are distributed tasks, return 1
							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							 =  self.count_ways_until(__a				,		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							 =  total_ways_util

							return self.dp[mask][task_no]




		def 						UpperCAmelCase							(					self				,		__a)       ->       int:






							'''simple docstring'''
							# Store the list of persons for each task
							for i in range(len(__a)):
												for j in task_performed[i]:
																	self.task[j].append(__a)

        # 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														=		5  # total no of tasks (the value of N)

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






