

from __future__ import annotations

from pathlib import Path





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





def  _snake_case		(snake_case_					:     int    ,       snake_case_					:     int    ,       snake_case_					:     int    ,       snake_case_					:     int    ,       snake_case_					:     int    ,       snake_case_					:     int  )							->		bool:
  __UpperCAmelCase	:  tuple[int, int]		=     (xa, ya)
  __UpperCAmelCase	:  tuple[int, int]		=     (xa - xa, ya - ya)
  __UpperCAmelCase	:  tuple[int, int]		=     (xa - xa, ya - ya)
  __UpperCAmelCase	:  float		=     -vector_product(snake_case_    ,       snake_case_  ) / vector_product(
      snake_case_    ,       snake_case_  )
  __UpperCAmelCase	:  float		=     +vector_product(snake_case_    ,       snake_case_  ) / vector_product(
      snake_case_    ,       snake_case_  )

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





def  _snake_case		(snake_case_					:     str = "p102_triangles.txt"  )							->		int:
  __UpperCAmelCase	:  str		=     Path(snake_case_  ).parent.joinpath(snake_case_  ).read_text(encoding='utf-8'  )

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

  __UpperCAmelCase	:  int		=     0
  __UpperCAmelCase	:  list[int]

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

  return ret


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









import tempfile
import unittest

import torch

from diffusers import UNetaDConditionModel
from diffusers.training_utils import EMAModel
from diffusers.utils.testing_utils import enable_full_determinism, skip_mps, torch_device


enable_full_determinism()



class      snake_case__	(   unittest.TestCase	):
				__lowerCAmelCase		=   '''hf-internal-testing/tiny-stable-diffusion-pipe'''
				__lowerCAmelCase		=   1
				__lowerCAmelCase		=   77
				__lowerCAmelCase		=   32
				__lowerCAmelCase		=   4
				__lowerCAmelCase		=   __lowerCAmelCase		=   64
				__lowerCAmelCase		=   torch.manual_seed(0	)
				def 			UpperCamelCase_    (	self  ,   _UpperCAmelCase=0.9999   ):




										"""simple docstring"""




										__magic_name__					:				List[Any]				=   UNetaDConditionModel.from_pretrained(self.model_id  ,   subfolder='unet'   )
										__magic_name__					:				int				=   unet.to(_UpperCAmelCase   )
										__magic_name__					:				Optional[int]				=   EMAModel(unet.parameters()  ,   decay=_UpperCAmelCase  ,   model_cls=_UpperCAmelCase  ,   model_config=unet.config   )
										return unet, ema_unet
				def 			UpperCamelCase_    (	self   ):




										"""simple docstring"""




										__magic_name__					:				List[str]				=   torch.randn(
										    self.batch_size  ,   self.num_in_channels  ,   self.latent_height  ,   self.latent_width  ,   generator=self.generator   ).to(_UpperCAmelCase   )
										__magic_name__					:				List[str]				=   torch.randint(0  ,   1000  ,   size=(self.batch_size,)  ,   generator=self.generator   ).to(_UpperCAmelCase   )
										__magic_name__					:				Any				=   torch.randn(
										    self.batch_size  ,   self.prompt_length  ,   self.text_encoder_hidden_dim  ,   generator=self.generator   ).to(_UpperCAmelCase   )
										return noisy_latents, timesteps, encoder_hidden_states
				def 			UpperCamelCase_    (	self  ,   _UpperCAmelCase   ):




										"""simple docstring"""




										__magic_name__					:				Any				=   {}
										for k, param in unet.state_dict().items():
																__magic_name__					:				str				=   torch.randn_like(_UpperCAmelCase   ) + (param * torch.randn_like(_UpperCAmelCase   ))
																updated_state_dict.update({k: updated_param}   )
										unet.load_state_dict(_UpperCAmelCase   )
										return unet
				def 			UpperCamelCase_    (	self   ):




										"""simple docstring"""




										__magic_name__		,			__magic_name__					:				int				=   self.get_models()
										# Take the first (hypothetical) EMA step.
										ema_unet.step(unet.parameters()   )
										assert ema_unet.optimization_step == 1

										# Take two more.
										for _ in range(2   ):
																ema_unet.step(unet.parameters()   )
										assert ema_unet.optimization_step == 3
				def 			UpperCamelCase_    (	self   ):




										"""simple docstring"""




										__magic_name__		,			__magic_name__					:				Union[str, Any]				=   self.get_models()
										# Since the `unet` is not being updated (i.e., backprop'd)
										# there won't be any difference between the `params` of `unet`
										# and `ema_unet` even if we call `ema_unet.step(unet.parameters())`.
										ema_unet.step(unet.parameters()   )
										__magic_name__					:				Any				=   list(unet.parameters()   )
										for s_param, param in zip(ema_unet.shadow_params  ,   _UpperCAmelCase   ):
																assert torch.allclose(_UpperCAmelCase  ,   _UpperCAmelCase   )

										# The above holds true even if we call `ema.step()` multiple times since
										# `unet` params are still not being updated.
										for _ in range(4   ):
																ema_unet.step(unet.parameters()   )
										for s_param, param in zip(ema_unet.shadow_params  ,   _UpperCAmelCase   ):
																assert torch.allclose(_UpperCAmelCase  ,   _UpperCAmelCase   )
				def 			UpperCamelCase_    (	self   ):




										"""simple docstring"""




										__magic_name__		,			__magic_name__					:				Optional[Any]				=   self.get_models()
										# Here we simulate the parameter updates for `unet`. Since there might
										# be some parameters which are initialized to zero we take extra care to
										# initialize their values to something non-zero before the multiplication.
										__magic_name__					:				Any				=   self.simulate_backprop(_UpperCAmelCase   )

										# Take the EMA step.
										ema_unet.step(unet_pseudo_updated_step_one.parameters()   )

										# Now the EMA'd parameters won't be equal to the original model parameters.
										__magic_name__					:				Any				=   list(unet_pseudo_updated_step_one.parameters()   )
										for s_param, param in zip(ema_unet.shadow_params  ,   _UpperCAmelCase   ):
																assert ~torch.allclose(_UpperCAmelCase  ,   _UpperCAmelCase   )

										# Ensure this is the case when we take multiple EMA steps.
										for _ in range(4   ):
																ema_unet.step(unet.parameters()   )
										for s_param, param in zip(ema_unet.shadow_params  ,   _UpperCAmelCase   ):
																assert ~torch.allclose(_UpperCAmelCase  ,   _UpperCAmelCase   )
				def 			UpperCamelCase_    (	self   ):




										"""simple docstring"""




										__magic_name__		,			__magic_name__					:				List[str]				=   self.get_models()

										# First backprop + EMA
										__magic_name__					:				int				=   self.simulate_backprop(_UpperCAmelCase   )
										ema_unet.step(unet_step_one.parameters()   )
										__magic_name__					:				Any				=   ema_unet.shadow_params

										# Second backprop + EMA
										__magic_name__					:				Any				=   self.simulate_backprop(_UpperCAmelCase   )
										ema_unet.step(unet_step_two.parameters()   )
										__magic_name__					:				Union[str, Any]				=   ema_unet.shadow_params

										for step_one, step_two in zip(_UpperCAmelCase  ,   _UpperCAmelCase   ):
																assert ~torch.allclose(_UpperCAmelCase  ,   _UpperCAmelCase   )
				def 			UpperCamelCase_    (	self   ):




										"""simple docstring"""




										__magic_name__		,			__magic_name__					:				Optional[Any]				=   self.get_models(decay=0.0   )
										__magic_name__					:				str				=   self.simulate_backprop(_UpperCAmelCase   )
										ema_unet.step(unet_step_one.parameters()   )
										__magic_name__					:				List[Any]				=   ema_unet.shadow_params

										__magic_name__					:				Optional[Any]				=   self.simulate_backprop(_UpperCAmelCase   )
										ema_unet.step(unet_step_two.parameters()   )
										__magic_name__					:				Optional[Any]				=   ema_unet.shadow_params

										for step_one, step_two in zip(_UpperCAmelCase  ,   _UpperCAmelCase   ):
																assert torch.allclose(_UpperCAmelCase  ,   _UpperCAmelCase   )





				@skip_mps
				def 			UpperCamelCase_    (	self   ):




										"""simple docstring"""




										__magic_name__		,			__magic_name__					:				Optional[int]				=   self.get_models()
										__magic_name__		,			__magic_name__		,			__magic_name__					:				str				=   self.get_dummy_inputs()

										with tempfile.TemporaryDirectory() as tmpdir:
																ema_unet.save_pretrained(_UpperCAmelCase   )
																__magic_name__					:				Optional[int]				=   UNetaDConditionModel.from_pretrained(_UpperCAmelCase  ,   model_cls=_UpperCAmelCase   )
																__magic_name__					:				str				=   loaded_unet.to(unet.device   )

										# Since no EMA step has been performed the outputs should match.
										__magic_name__					:				Union[str, Any]				=   unet(_UpperCAmelCase  ,   _UpperCAmelCase  ,   _UpperCAmelCase   ).sample
										__magic_name__					:				List[Any]				=   loaded_unet(_UpperCAmelCase  ,   _UpperCAmelCase  ,   _UpperCAmelCase   ).sample

										assert torch.allclose(_UpperCAmelCase  ,   _UpperCAmelCase  ,   atol=1E-4   )


