'''simple docstring'''




from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt




def 							lowerCamelCase			(   UpperCAmelCase__ :      int				)    ->   bool:
							lowercase_      :    int       		= int(number**0.5				)
							return number == sq * sq




def 							lowerCamelCase			(   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int				)    ->   tuple[int, int]:
							lowercase_      :    int       		= x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
							lowercase_      :    int       		= x_den * y_den * z_den
							lowercase_      :    int       		= gcd(UpperCAmelCase__   ,   UpperCAmelCase__				)
							top //= hcf
							bottom //= hcf
							return top, bottom




def 							lowerCamelCase			(   UpperCAmelCase__ :      int = 35				)    ->   int:
							lowercase_      :    set       		= set()
							lowercase_      :    int
							lowercase_      :    Fraction       		= Fraction(0				)
							lowercase_      :    tuple[int, int]

							for x_num in range(1   ,   order + 1				):
														for x_den in range(x_num + 1   ,   order + 1				):
																					for y_num in range(1   ,   order + 1				):
																												for y_den in range(y_num + 1   ,   order + 1				):
																																			# n=1
																																			lowercase_      :    str       		= x_num * y_den + x_den * y_num
																																			lowercase_      :    Optional[int]       		= x_den * y_den
																																			lowercase_      :    Optional[int]       		= gcd(UpperCAmelCase__   ,   UpperCAmelCase__				)
																																			z_num //= hcf
																																			z_den //= hcf
																																			if 0 < z_num < z_den <= order:
																																										lowercase_      :    List[str]       		= add_three(
																																										    UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__				)
																																										unique_s.add(UpperCAmelCase__				)

																																			# n=2
																																			lowercase_      :    List[str]       		= (
																																			    x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
																																			)
																																			lowercase_      :    Optional[int]       		= x_den * x_den * y_den * y_den
																																			if is_sq(UpperCAmelCase__				) and is_sq(UpperCAmelCase__				):
																																										lowercase_      :    Optional[Any]       		= int(sqrt(UpperCAmelCase__				)				)
																																										lowercase_      :    Optional[Any]       		= int(sqrt(UpperCAmelCase__				)				)
																																										lowercase_      :    List[Any]       		= gcd(UpperCAmelCase__   ,   UpperCAmelCase__				)
																																										z_num //= hcf
																																										z_den //= hcf
																																										if 0 < z_num < z_den <= order:
																																																	lowercase_      :    List[Any]       		= add_three(
																																																	    UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__				)
																																																	unique_s.add(UpperCAmelCase__				)

                    # n=-1
																																			lowercase_      :    List[Any]       		= x_num * y_num
																																			lowercase_      :    Any       		= x_den * y_num + x_num * y_den
																																			lowercase_      :    Any       		= gcd(UpperCAmelCase__   ,   UpperCAmelCase__				)
																																			z_num //= hcf
																																			z_den //= hcf
																																			if 0 < z_num < z_den <= order:
																																										lowercase_      :    List[Any]       		= add_three(
																																										    UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__				)
																																										unique_s.add(UpperCAmelCase__				)

																																			# n=2
																																			lowercase_      :    str       		= x_num * x_num * y_num * y_num
																																			lowercase_      :    Tuple       		= (
																																			    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
																																			)
																																			if is_sq(UpperCAmelCase__				) and is_sq(UpperCAmelCase__				):
																																										lowercase_      :    Optional[Any]       		= int(sqrt(UpperCAmelCase__				)				)
																																										lowercase_      :    int       		= int(sqrt(UpperCAmelCase__				)				)
																																										lowercase_      :    Optional[int]       		= gcd(UpperCAmelCase__   ,   UpperCAmelCase__				)
																																										z_num //= hcf
																																										z_den //= hcf
																																										if 0 < z_num < z_den <= order:
																																																	lowercase_      :    List[str]       		= add_three(
																																																	    UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__				)
																																																	unique_s.add(UpperCAmelCase__				)

							for num, den in unique_s:
														total += Fraction(UpperCAmelCase__   ,   UpperCAmelCase__				)

							return total.denominator + total.numerator


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






'''simple docstring'''




import argparse

import intel_extension_for_pytorch as ipex
import torch

from diffusers import DPMSolverMultistepScheduler, StableDiffusionPipeline


_lowercase		:				Optional[Any]	       =		argparse.ArgumentParser("Stable Diffusion script with intel optimization", add_help=False)
parser.add_argument("--dpm", action="store_true", help="Enable DPMSolver or not")
parser.add_argument("--steps", default=None, type=int, help="Num inference steps")
_lowercase		:				Dict	       =		parser.parse_args()


_lowercase		:				Dict	       =		"cpu"
_lowercase		:				str	       =		"a lovely <dicoo> in red dress and hat, in the snowly and brightly night, with many brighly buildings"

_lowercase		:				Any	       =		"path-to-your-trained-model"
_lowercase		:				str	       =		StableDiffusionPipeline.from_pretrained(model_id)
if args.dpm:
						_lowercase		:				Optional[int]	       =		DPMSolverMultistepScheduler.from_config(pipe.scheduler.config)
_lowercase		:				Any	       =		pipe.to(device)

# to channels last
_lowercase		:				Union[str, Any]	       =		pipe.unet.to(memory_format=torch.channels_last)
_lowercase		:				List[Any]	       =		pipe.vae.to(memory_format=torch.channels_last)
_lowercase		:				Union[str, Any]	       =		pipe.text_encoder.to(memory_format=torch.channels_last)
if pipe.requires_safety_checker:
						_lowercase		:				Tuple	       =		pipe.safety_checker.to(memory_format=torch.channels_last)

# optimize with ipex
_lowercase		:				int	       =		torch.randn(2, 4, 64, 64)
_lowercase		:				int	       =		torch.rand(1) * 999
_lowercase		:				Union[str, Any]	       =		torch.randn(2, 77, 768)
_lowercase		:				Optional[Any]	       =		(sample, timestep, encoder_hidden_status)
try:
						_lowercase		:				int	       =		ipex.optimize(pipe.unet.eval(), dtype=torch.bfloataa, inplace=True, sample_input=input_example)
except Exception:
						_lowercase		:				Optional[int]	       =		ipex.optimize(pipe.unet.eval(), dtype=torch.bfloataa, inplace=True)
_lowercase		:				List[Any]	       =		ipex.optimize(pipe.vae.eval(), dtype=torch.bfloataa, inplace=True)
_lowercase		:				str	       =		ipex.optimize(pipe.text_encoder.eval(), dtype=torch.bfloataa, inplace=True)
if pipe.requires_safety_checker:
						_lowercase		:				int	       =		ipex.optimize(pipe.safety_checker.eval(), dtype=torch.bfloataa, inplace=True)

# compute
_lowercase		:				int	       =		666
_lowercase		:				Any	       =		torch.Generator(device).manual_seed(seed)
_lowercase		:				int	       =		{"generator": generator}
if args.steps is not None:
						_lowercase		:				Optional[int]	       =		args.steps

with torch.cpu.amp.autocast(enabled=True, dtype=torch.bfloataa):
						_lowercase		:				List[Any]	       =		pipe(prompt, **generate_kwargs).images[0]

# save image
image.save("generated.png")





