
"""simple docstring"""


import torch

from transformers import AutoTokenizer







class 						lowerCamelCase__   (   __magic_name__							):





			'''simple docstring'''



			def __init__(				self	,	__UpperCAmelCase    )					->	Optional[int]:
				_lowerCAmelCase								=AutoTokenizer.from_pretrained(__UpperCAmelCase    )



			def    _lowerCAmelCase						(				self	,	__UpperCAmelCase    )					->	Optional[Any]:

				if isinstance(__UpperCAmelCase	,	__UpperCAmelCase    ) and all(isinstance(_x	,	__UpperCAmelCase    ) for _x in x    ):
					_lowerCAmelCase								=None
					for l in x:
						_lowerCAmelCase								=self.tokenizer(
						    __UpperCAmelCase	,	padding="""max_length"""	,	max_length=3_84	,	truncation=__UpperCAmelCase	,	return_tensors="""pt"""	,	)
						_lowerCAmelCase								=torch.tensor([len(__UpperCAmelCase    )]    )
						if d is not None:
							for k in d.keys():
								_lowerCAmelCase								=torch.cat((d[k], t[k])	,	0    )
						else:
							_lowerCAmelCase								=t

					_lowerCAmelCase								=torch.tensor(self.tokenizer.convert_tokens_to_ids("""[E]"""    )    )
					_lowerCAmelCase								=torch.tensor(self.tokenizer.convert_tokens_to_ids("""[/E]"""    )    )

				elif isinstance(__UpperCAmelCase	,	__UpperCAmelCase    ) and all(isinstance(_x	,	__UpperCAmelCase    ) for _x in x    ):
					_lowerCAmelCase								=self.tokenizer(
					    __UpperCAmelCase	,	padding="""max_length"""	,	max_length=3_84	,	truncation=__UpperCAmelCase	,	return_tensors="""pt"""	,	)

				else:
					raise Exception(
					    """Type of parameter x was not recognized! Only `list of strings` for query or `list of lists of"""
					    """ strings` for supports are supported."""    )

				return d



			def    _lowerCAmelCase						(				self	,	__UpperCAmelCase	,	__UpperCAmelCase	,	__UpperCAmelCase	,	__UpperCAmelCase	,	__UpperCAmelCase=0.7_0    )					->	Dict:
				_lowerCAmelCase								=[]
				for idx in range(len(W_query["""input_ids"""]    )    ):
					_lowerCAmelCase								=_lowerCAmelCase								=range(p_start.shape[1]    )

					_lowerCAmelCase								=[]
					for start_id in start_indexes:
						for end_id in end_indexes:
							if start_id < end_id:
								output.append(
								    (
								        start_id,
								        end_id,
								        p_start[idx][start_id].item(),
								        p_end[idx][end_id].item(),
								    )    )

					output.sort(key=lambda __UpperCAmelCase    : (tup[2] * tup[3])	,	reverse=__UpperCAmelCase    )
					_lowerCAmelCase								=[]
					for k in range(len(__UpperCAmelCase    )    ):
						if output[k][2] * output[k][3] >= thresh:
							_lowerCAmelCase		,				_lowerCAmelCase								=output[k][0], output[k][1]
							_lowerCAmelCase								=self.tokenizer.decode(W_query["""input_ids"""][idx][c_start_pos:c_end_pos]    )
							temp.append((decoded, output[k][2] * output[k][3])    )

					final_outputs.append(__UpperCAmelCase    )

				return final_outputs





"""simple docstring"""


import math



def        _lowerCamelCase(__UpperCamelCase			)							->					bool:

	if 1 < number < 4:
		# 2 and 3 are primes
		return True
	elif number < 2 or number % 2 == 0 or number % 3 == 0:
		# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
		return False

	# All primes number are in format of 6k +/- 1
	for i in range(5       ,					int(math.sqrt(__UpperCamelCase			) + 1			)       ,					6			):
		if number % i == 0 or number % (i + 2) == 0:
			return False
	return True



def        _lowerCamelCase(__UpperCamelCase = 600851475143			)							->					int:

	try:
		_lowerCAmelCase								=int(__UpperCamelCase			)
	except (TypeError, ValueError):
		raise TypeError("""Parameter n must be int or castable to int."""			)
	if n <= 0:
		raise ValueError("""Parameter n must be greater than or equal to one."""			)
	_lowerCAmelCase								=0
	if is_prime(__UpperCamelCase			):
		return n
	while n % 2 == 0:
		n //= 2
	if is_prime(__UpperCamelCase			):
		return n
	for i in range(3       ,					int(math.sqrt(__UpperCamelCase			)			) + 1       ,					2			):
		if n % i == 0:
			if is_prime(n // i			):
				_lowerCAmelCase								=n // i
				break
			elif is_prime(__UpperCamelCase			):
				_lowerCAmelCase								=i
	return max_number


if __name__ == "__main__":
			print(F"""{solution() = }""")



