
"""simple docstring"""




import torch

from accelerate import Accelerator, DistributedType




class 	UpperCamelCase      :

				"""simple docstring"""



				def __enter__(							self     )       ->       int:
									"""simple docstring"""







									if self.enabled:
														SCREAMING_SNAKE_CASE           =      self.model.no_sync()
														self.model_sync_obj.__enter__()

									return self


				def __exit__(							self						,      lowercase__						,      lowercase__						,      lowercase__     )       ->       Optional[int]:
									"""simple docstring"""







									if self.enabled:
														# Average all models on exit
														self._sync_and_avg_model_params()
														self.model_sync_obj.__exit__(lowercase__						,      lowercase__						,      lowercase__     )


				def __init__(							self						,      lowercase__						,      lowercase__						,      lowercase__						,      lowercase__ = True     )       ->       List[Any]:
									"""simple docstring"""







									if accelerator.distributed_type not in [
									    DistributedType.NO,
									    DistributedType.MULTI_CPU,
									    DistributedType.MULTI_GPU,
									]:
														raise NotImplementedError('LocalSGD is supported only for CPUs and GPUs (no DeepSpeed or MegatronLM)'     )
									SCREAMING_SNAKE_CASE           =      enabled and accelerator.distributed_type != DistributedType.NO
									SCREAMING_SNAKE_CASE           =      0
									if self.enabled:
														SCREAMING_SNAKE_CASE           =      accelerator
														SCREAMING_SNAKE_CASE           =      model
														SCREAMING_SNAKE_CASE           =      local_sgd_steps


				def 				A   (							self     )       ->       str:
									"""simple docstring"""







									self.num_steps += 1
									if not self.enabled:
														return

									if self.num_steps % self.local_sgd_steps == 0:
														self._sync_and_avg_model_params()




				def 				A   (							self     )       ->       Dict:
									"""simple docstring"""







									self.accelerator.wait_for_everyone()
									with self.accelerator.autocast():
														for param in self.model.parameters():
																			SCREAMING_SNAKE_CASE           =      self.accelerator.reduce(param.data						,      reduction='mean'     )



'''simple docstring'''







from __future__ import annotations

from pathlib import Path






def 					_SCREAMING_SNAKE_CASE		(						snake_case_							,       snake_case_	):
	return pointa[0] * pointa[1] - pointa[1] * pointa[0]






def 					_SCREAMING_SNAKE_CASE		(						snake_case_							,       snake_case_							,       snake_case_							,       snake_case_							,       snake_case_							,       snake_case_	):
	_lowercase							=     (xa, ya)
	_lowercase							=     (xa - xa, ya - ya)
	_lowercase							=     (xa - xa, ya - ya)
	_lowercase							=     -vector_product(snake_case_							,       snake_case_	) / vector_product(
	    snake_case_							,       snake_case_	)
	_lowercase							=     +vector_product(snake_case_							,       snake_case_	) / vector_product(
	    snake_case_							,       snake_case_	)

	return a > 0 and b > 0 and a + b < 1






def 					_SCREAMING_SNAKE_CASE		(						snake_case_ = "p102_triangles.txt"	):
	_lowercase							=     Path(snake_case_	).parent.joinpath(snake_case_	).read_text(encoding="""utf-8"""	)

	_lowercase							=     []
	for line in data.strip().split("""\n"""	):
		triangles.append([int(snake_case_	) for number in line.split(""","""	)]	)

	_lowercase							=     0
	_lowercase							=     42

	for triangle in triangles:
		ret += contains_origin(*snake_case_	)

	return ret


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




