






from typing import List, Optional, Tuple, Union

from . import logging
from .import_utils import is_torch_available, is_torch_version


if is_torch_available():
			import torch

UpperCAmelCase__			 =	logging.get_logger(__name__)  # pylint: disable=invalid-name

try:
			from torch._dynamo import allow_in_graph as maybe_allow_in_graph
except (ImportError, ModuleNotFoundError):







			def 						a_      (cls			)							->	Optional[int]:



								"""simple docstring"""
								return cls







def 						a_      (__A							,					__A = None							,					__A = None							,					__A = None							,					__A = None							,					)							->	Optional[Any]:



					"""simple docstring"""
					__a				:	Dict			=				device
					__a				:	Tuple			=				shape[0]

					__a				:	Union[str, Any]			=				layout or torch.strided
					__a				:	Dict			=				device or torch.device("cpu"			)

					if generator is not None:
										__a				:	Optional[int]			=				generator.device.type if not isinstance(__A							,					__A			) else generator[0].device.type
										if gen_device_type != device.type and gen_device_type == "cpu":
															__a				:	List[str]			=				"cpu"
															if device != "mps":
																				logger.info(
																				    f'The passed generator was created on \'cpu\' even though a tensor on {device} was expected.'
																				    f' Tensors will be created on \'cpu\' and then moved to {device}. Note that one can probably'
																				    f' slighly speed up this function by passing a generator that was created on the {device} device.'			)
										elif gen_device_type != device.type and gen_device_type == "cuda":
															raise ValueError(f'Cannot generate a {device} tensor from a generator of type {gen_device_type}.'			)

					if isinstance(__A							,					__A			):
										__a				:	Tuple			=				(1,) + shape[1:]
										__a				:	str			=				[
										    torch.randn(__A							,					generator=generator[i]							,					device=__A							,					dtype=__A							,					layout=__A			)
										    for i in range(__A			)
										]
										__a				:	Dict			=				torch.cat(__A							,					dim=0			).to(__A			)
					else:
										__a				:	Optional[Any]			=				torch.randn(__A							,					generator=__A							,					device=__A							,					dtype=__A							,					layout=__A			).to(__A			)

					return latents







def 						a_      (__A			)							->	List[Any]:



					"""simple docstring"""



					if is_torch_version("<"							,					"2.0.0"			) or not hasattr(__A							,					"_dynamo"			):
										return False
					return isinstance(__A							,					torch._dynamo.eval_frame.OptimizedModule			)












import math







def 						a_      (__A			)							->	bool:



					"""simple docstring"""

					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(__A			) + 1			)							,					6			):
										if number % i == 0 or number % (i + 2) == 0:
															return False
					return True







def 						a_      (__A = 1_000							,					__A = 1_000			)							->	int:



					"""simple docstring"""
					__a				:	Optional[int]			=				[0, 0, 0]  # length, a, b
					for a in range((a_limit * -1) + 1							,					__A			):
										for b in range(2							,					__A			):
															if is_prime(__A			):
																				__a				:	Any			=				0
																				__a				:	List[str]			=				0
																				while is_prime((n**2) + (a * n) + b			):
																									count += 1
																									n += 1
																				if count > longest[0]:
																									__a				:	Any			=				[count, a, b]
					__a				:	str			=				longest[1] * longest[2]
					return ans


if __name__ == "__main__":
			print(solution(1000, 1000))





