"""simple docstring"""




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      UpperCamelCase__(      unittest.TestCase			):
						lowerCAmelCase__	:    str    				=		"""hf-internal-testing/tiny-stable-diffusion-pipe"""
						lowerCAmelCase__	:    Union[str, Any]    				=		1
						lowerCAmelCase__	:    Tuple    				=		77
						lowerCAmelCase__	:    int    				=		32
						lowerCAmelCase__	:    Union[str, Any]    				=		4
						lowerCAmelCase__	:    Dict    				=		64
						lowerCAmelCase__	:    str    				=		torch.manual_seed(0			)





						def 					snake_case__						(							self		,__UpperCAmelCase=0.9_9_9_9  )       ->					List[str]:
													A__						  =				UNetaDConditionModel.from_pretrained(self.model_id		,subfolder='unet'  )
													A__						  =				unet.to(lowerCamelCase__  )
													A__						  =				EMAModel(unet.parameters()		,decay=lowerCamelCase__		,model_cls=lowerCamelCase__		,model_config=unet.config  )
													return unet, ema_unet





						def 					snake_case__						(							self  )       ->					List[str]:
													A__						  =				torch.randn(
													    self.batch_size		,self.num_in_channels		,self.latent_height		,self.latent_width		,generator=self.generator  ).to(lowerCamelCase__  )
													A__						  =				torch.randint(0		,10_00		,size=(self.batch_size,)		,generator=self.generator  ).to(lowerCamelCase__  )
													A__						  =				torch.randn(
													    self.batch_size		,self.prompt_length		,self.text_encoder_hidden_dim		,generator=self.generator  ).to(lowerCamelCase__  )
													return noisy_latents, timesteps, encoder_hidden_states





						def 					snake_case__						(							self		,__UpperCAmelCase  )       ->					Any:
													A__						  =				{}
													for k, param in unet.state_dict().items():
																				A__						  =				torch.randn_like(lowerCamelCase__  ) + (param * torch.randn_like(lowerCamelCase__  ))
																				updated_state_dict.update({k: updated_param}  )
													unet.load_state_dict(lowerCamelCase__  )
													return unet





						def 					snake_case__						(							self  )       ->					List[Any]:
													A__  ,	A__						  =				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 					snake_case__						(							self  )       ->					str:
													A__  ,	A__						  =				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()  )
													A__						  =				list(unet.parameters()  )
													for s_param, param in zip(ema_unet.shadow_params		,lowerCamelCase__  ):
																				assert torch.allclose(lowerCamelCase__		,lowerCamelCase__  )

													# 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		,lowerCamelCase__  ):
																				assert torch.allclose(lowerCamelCase__		,lowerCamelCase__  )





						def 					snake_case__						(							self  )       ->					int:
													A__  ,	A__						  =				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.
													A__						  =				self.simulate_backprop(lowerCamelCase__  )

													# 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.
													A__						  =				list(unet_pseudo_updated_step_one.parameters()  )
													for s_param, param in zip(ema_unet.shadow_params		,lowerCamelCase__  ):
																				assert ~torch.allclose(lowerCamelCase__		,lowerCamelCase__  )

													# 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		,lowerCamelCase__  ):
																				assert ~torch.allclose(lowerCamelCase__		,lowerCamelCase__  )





						def 					snake_case__						(							self  )       ->					Optional[int]:
													A__  ,	A__						  =				self.get_models()

													# First backprop + EMA
													A__						  =				self.simulate_backprop(lowerCamelCase__  )
													ema_unet.step(unet_step_one.parameters()  )
													A__						  =				ema_unet.shadow_params

													# Second backprop + EMA
													A__						  =				self.simulate_backprop(lowerCamelCase__  )
													ema_unet.step(unet_step_two.parameters()  )
													A__						  =				ema_unet.shadow_params

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





						def 					snake_case__						(							self  )       ->					Union[str, Any]:
													A__  ,	A__						  =				self.get_models(decay=0.0  )
													A__						  =				self.simulate_backprop(lowerCamelCase__  )
													ema_unet.step(unet_step_one.parameters()  )
													A__						  =				ema_unet.shadow_params

													A__						  =				self.simulate_backprop(lowerCamelCase__  )
													ema_unet.step(unet_step_two.parameters()  )
													A__						  =				ema_unet.shadow_params

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





						@skip_mps
						def 					snake_case__						(							self  )       ->					List[str]:
													A__  ,	A__						  =				self.get_models()
													A__  ,	A__  ,	A__						  =				self.get_dummy_inputs()

													with tempfile.TemporaryDirectory() as tmpdir:
																				ema_unet.save_pretrained(lowerCamelCase__  )
																				A__						  =				UNetaDConditionModel.from_pretrained(lowerCamelCase__		,model_cls=lowerCamelCase__  )
																				A__						  =				loaded_unet.to(unet.device  )

													# Since no EMA step has been performed the outputs should match.
													A__						  =				unet(lowerCamelCase__		,lowerCamelCase__		,lowerCamelCase__  ).sample
													A__						  =				loaded_unet(lowerCamelCase__		,lowerCamelCase__		,lowerCamelCase__  ).sample

													assert torch.allclose(lowerCamelCase__		,lowerCamelCase__		,atol=1e-4  )











'''simple docstring'''
from math import gcd
def 							snake_case_    (  a__						:      int = 1_20_00     ):



    """simple docstring"""




    __lowercase     							=		0
    for d in range(max_d + 1     ):
        for n in range(d // 3 + 1       ,(d + 1) // 2     ):
            if gcd(a__       ,a__     ) == 1:
                fractions_number += 1
    return fractions_number


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




