


'''simple docstring'''

lowerCamelCase							:   List[Any]  						=	{
    'Pillow': 'Pillow',
    'accelerate': 'accelerate>=0.11.0',
    'compel': 'compel==0.1.8',
    'black': 'black~=23.1',
    'datasets': 'datasets',
    'filelock': 'filelock',
    'flax': 'flax>=0.4.1',
    'hf-doc-builder': 'hf-doc-builder>=0.3.0',
    'huggingface-hub': 'huggingface-hub>=0.13.2',
    'requests-mock': 'requests-mock==1.10.0',
    'importlib_metadata': 'importlib_metadata',
    'invisible-watermark': 'invisible-watermark',
    'isort': 'isort>=5.5.4',
    'jax': 'jax>=0.2.8,!=0.3.2',
    'jaxlib': 'jaxlib>=0.1.65',
    'Jinja2': 'Jinja2',
    'k-diffusion': 'k-diffusion>=0.0.12',
    'torchsde': 'torchsde',
    'note_seq': 'note_seq',
    'librosa': 'librosa',
    'numpy': 'numpy',
    'omegaconf': 'omegaconf',
    'parameterized': 'parameterized',
    'protobuf': 'protobuf>=3.20.3,<4',
    'pytest': 'pytest',
    'pytest-timeout': 'pytest-timeout',
    'pytest-xdist': 'pytest-xdist',
    'ruff': 'ruff>=0.0.241',
    'safetensors': 'safetensors',
    'sentencepiece': 'sentencepiece>=0.1.91,!=0.1.92',
    'scipy': 'scipy',
    'onnx': 'onnx',
    'regex': 'regex!=2019.12.17',
    'requests': 'requests',
    'tensorboard': 'tensorboard',
    'torch': 'torch>=1.4',
    'torchvision': 'torchvision',
    'transformers': 'transformers>=4.25.1',
    'urllib3': 'urllib3<=2.0.0',
}






"""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
				    )
				)






