"""simple docstring"""







from __future__ import annotations

from pathlib import Path



def       A__    (	lowercase_     :	tuple[int, int]      , lowercase_     :	tuple[int, int]						)  ->							int:
   return pointa[0] * pointa[1] - pointa[1] * pointa[0]



def       A__    (	lowercase_     :	int      , lowercase_     :	int      , lowercase_     :	int      , lowercase_     :	int      , lowercase_     :	int      , lowercase_     :	int						)  ->							bool:
   __lowerCamelCase    		=					(xa, ya)
   __lowerCamelCase    		=					(xa - xa, ya - ya)
   __lowerCamelCase    		=					(xa - xa, ya - ya)
   __lowerCamelCase    		=					-vector_product(lowercase_      , lowercase_						) / vector_product(
       lowercase_      , lowercase_						)
   __lowerCamelCase    		=					+vector_product(lowercase_      , lowercase_						) / vector_product(
       lowercase_      , lowercase_						)

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



def       A__    (	lowercase_     :	str = "p102_triangles.txt"						)  ->							int:
   __lowerCamelCase    		=					Path(lowercase_						).parent.joinpath(lowercase_						).read_text(encoding='utf-8'						)

   __lowerCamelCase    		=					[]
   for line in data.strip().split('\n'						):
      triangles.append([int(lowercase_						) for number in line.split(','						)]						)

   __lowerCamelCase    		=					0
   __lowerCamelCase    		=					42

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

   return ret


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








from typing import List, Optional, Tuple, Union

import torch

from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput







class 	A__				(	__magic_name__      ):






				def __init__(		self   : Any       ,	a   : Any       ,	a   : Optional[int]  ):






							'''simple docstring'''







							super().__init__()
							self.register_modules(unet=a       ,	scheduler=a  )






				@torch.no_grad()
				def __call__(		self   : Optional[Any]       ,	a   : int = 1       ,	a   : Optional[Union[torch.Generator, List[torch.Generator]]] = None       ,	a   : int = 1_000       ,	a   : Optional[str] = "pil"       ,	a   : bool = True       ,	):






							'''simple docstring'''







							if isinstance(self.unet.config.sample_size       ,	a  ):
										lowerCAmelCase__ : Union[str, Any]   =						(
										    batch_size,
										    self.unet.config.in_channels,
										    self.unet.config.sample_size,
										    self.unet.config.sample_size,
										)
							else:
										lowerCAmelCase__ : str   =						(batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

							if self.device.type == "mps":
										# randn does not work reproducibly on mps
										lowerCAmelCase__ : Optional[int]   =						randn_tensor(a       ,	generator=a  )
										lowerCAmelCase__ : Optional[int]   =						image.to(self.device  )
							else:
										lowerCAmelCase__ : Dict   =						randn_tensor(a       ,	generator=a       ,	device=self.device  )

							# set step values
							self.scheduler.set_timesteps(a  )

							for t in self.progress_bar(self.scheduler.timesteps  ):
										# 1. predict noise model_output
										lowerCAmelCase__ : Tuple   =						self.unet(a       ,	a  ).sample

										# 2. compute previous image: x_t -> x_t-1
										lowerCAmelCase__ : Optional[Any]   =						self.scheduler.step(a       ,	a       ,	a       ,	generator=a  ).prev_sample

							lowerCAmelCase__ : str   =						(image / 2 + 0.5).clamp(0       ,	1  )
							lowerCAmelCase__ : Optional[int]   =						image.cpu().permute(0       ,	2       ,	3       ,	1  ).numpy()
							if output_type == "pil":
										lowerCAmelCase__ : int   =						self.numpy_to_pil(a  )

							if not return_dict:
										return (image,)

							return ImagePipelineOutput(images=a  )