"""simple docstring"""




from typing import List

import numpy as np







def 							_UpperCAmelCase		(       lowerCamelCase__     ):





		"""simple docstring"""




		lowerCAmelCase__        =   {key: len(lowerCamelCase__     ) for key, value in gen_kwargs.items() if isinstance(lowerCamelCase__			,  lowerCamelCase__     )}
		if len(set(lists_lengths.values()     )     ) > 1:
				raise RuntimeError(
				    (
				        """Sharding is ambiguous for this dataset: """
				        + """we found several data sources lists of different lengths, and we don't know over which list we should parallelize:\n"""
				        + """\n""".join(f"""\t- key {key} has length {length}""" for key, length in lists_lengths.items()     )
				        + """\nTo fix this, check the 'gen_kwargs' and make sure to use lists only for data sources, """
				        + """and use tuples otherwise. In the end there should only be one single list, or several lists with the same length."""
				    )     )
		lowerCAmelCase__        =   max(lists_lengths.values()			,  default=0     )
		return max(1			,  lowerCamelCase__     )







def 							_UpperCAmelCase		(       lowerCamelCase__			,  lowerCamelCase__     ):





		"""simple docstring"""




		lowerCAmelCase__        =   []
		for group_idx in range(lowerCamelCase__     ):
				lowerCAmelCase__        =   num_shards // max_num_jobs + (group_idx < (num_shards % max_num_jobs))
				if num_shards_to_add == 0:
						break
				lowerCAmelCase__        =   shards_indices_per_group[-1].stop if shards_indices_per_group else 0
				lowerCAmelCase__        =   range(lowerCamelCase__			,  start + num_shards_to_add     )
				shards_indices_per_group.append(lowerCamelCase__     )
		return shards_indices_per_group







def 							_UpperCAmelCase		(       lowerCamelCase__			,  lowerCamelCase__     ):





		"""simple docstring"""




		lowerCAmelCase__        =   _number_of_shards_in_gen_kwargs(lowerCamelCase__     )
		if num_shards == 1:
				return [dict(lowerCamelCase__     )]
		else:
				lowerCAmelCase__        =   _distribute_shards(num_shards=lowerCamelCase__			,  max_num_jobs=lowerCamelCase__     )
				return [
				    {
				        key: [value[shard_idx] for shard_idx in shard_indices_per_group[group_idx]]
				        if isinstance(lowerCamelCase__			,  lowerCamelCase__     )
				        else value
				        for key, value in gen_kwargs.items()
				    }
				    for group_idx in range(len(lowerCamelCase__     )     )
				]







def 							_UpperCAmelCase		(       lowerCamelCase__     ):





		"""simple docstring"""




		return {
		    key: [value for gen_kwargs in gen_kwargs_list for value in gen_kwargs[key]]
		    if isinstance(gen_kwargs_list[0][key]			,  lowerCamelCase__     )
		    else gen_kwargs_list[0][key]
		    for key in gen_kwargs_list[0]
		}







def 							_UpperCAmelCase		(       lowerCamelCase__			,  lowerCamelCase__     ):





		"""simple docstring"""




		lowerCAmelCase__        =   {len(lowerCamelCase__     ) for value in gen_kwargs.values() if isinstance(lowerCamelCase__			,  lowerCamelCase__     )}
		lowerCAmelCase__        =   {}
		for size in list_sizes:
				lowerCAmelCase__        =   list(range(lowerCamelCase__     )     )
				rng.shuffle(indices_per_size[size]     )
		# Now let's copy the gen_kwargs and shuffle the lists based on their sizes
		lowerCAmelCase__        =   dict(lowerCamelCase__     )
		for key, value in shuffled_kwargs.items():
				if isinstance(lowerCamelCase__			,  lowerCamelCase__     ):
						lowerCAmelCase__        =   [value[i] for i in indices_per_size[len(lowerCamelCase__     )]]
		return shuffled_kwargs





"""simple docstring"""




from math import pi, sqrt







def 							_UpperCAmelCase		(       lowerCamelCase__     ):





		"""simple docstring"""




		if num <= 0:
				raise ValueError("""math domain error"""     )
		if num > 1_71.5:
				raise OverflowError("""math range error"""     )
		elif num - int(lowerCamelCase__     ) not in (0, 0.5):
				raise NotImplementedError("""num must be an integer or a half-integer"""     )
		elif num == 0.5:
				return sqrt(lowerCamelCase__     )
		else:
				return 1.0 if num == 1 else (num - 1) * gamma(num - 1     )







def 							_UpperCAmelCase		(       ):





		"""simple docstring"""




		assert gamma(0.5     ) == sqrt(lowerCamelCase__     )
		assert gamma(1     ) == 1.0
		assert gamma(2     ) == 1.0


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

			testmod()
			__lowerCAmelCase    :							Dict													=						1.0
			while num:
						__lowerCAmelCase    :							Any													=						float(input("Gamma of: "))
						print(F"gamma({num}) = {gamma(num)}")
						print("\nEnter 0 to exit...")




