


'''simple docstring'''



from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int   ):
					__a			:       int					    =  int(number**0.5   )
					return number == sq * sq






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int   ):
					__a			:       int					    =  x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
					__a			:       int					    =  x_den * y_den * z_den
					__a			:       int					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
					top //= hcf
					bottom //= hcf
					return top, bottom






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int = 35   ):
					__a			:       set					    =  set()
					__a			:       int
					__a			:       Fraction					    =  Fraction(0   )
					__a			:       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
																									__a			:       Union[str, Any]					    =  x_num * y_den + x_den * y_num
																									__a			:       Optional[Any]					    =  x_den * y_den
																									__a			:       int					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														__a			:       Any					    =  add_three(
																														    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														unique_s.add(_SCREAMING_SNAKE_CASE   )

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

                    # n=-1
																									__a			:       int					    =  x_num * y_num
																									__a			:       Optional[Any]					    =  x_den * y_num + x_num * y_den
																									__a			:       Tuple					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														__a			:       Any					    =  add_three(
																														    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														unique_s.add(_SCREAMING_SNAKE_CASE   )

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

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

					return total.denominator + total.numerator


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







'''simple docstring'''



import gc
import random
import unittest

import numpy as np
import torch
from PIL import Image
from transformers import CLIPTextConfig, CLIPTextModel, CLIPTokenizer

from diffusers import AutoencoderKL, PNDMScheduler, StableDiffusionInpaintPipeline, UNetaDConditionModel
from diffusers.utils import floats_tensor, load_image, load_numpy, torch_device
from diffusers.utils.testing_utils import enable_full_determinism, require_torch_gpu, slow

from ..pipeline_params import TEXT_GUIDED_IMAGE_INPAINTING_BATCH_PARAMS, TEXT_GUIDED_IMAGE_INPAINTING_PARAMS
from ..test_pipelines_common import PipelineKarrasSchedulerTesterMixin, PipelineLatentTesterMixin, PipelineTesterMixin


enable_full_determinism()





class 							__UpperCamelCase				(		lowerCAmelCase_		,      lowerCAmelCase_		,      lowerCAmelCase_		,      unittest.TestCase					):
	A_				=    StableDiffusionInpaintPipeline
	A_				=    TEXT_GUIDED_IMAGE_INPAINTING_PARAMS
	A_				=    TEXT_GUIDED_IMAGE_INPAINTING_BATCH_PARAMS
	A_				=    frozenset(
	    []					)  # TO-DO: update image_params once pipeline is refactored with VaeImageProcessor.preprocess
	A_				=    frozenset([]					)




	def       __UpperCAmelCase							(   self							):

						'''simple docstring'''





						torch.manual_seed(0							)
						__a			:       int					    =  UNetaDConditionModel(
						    block_out_channels=(32, 64)						,				layers_per_block=2						,				sample_size=32						,				in_channels=9						,				out_channels=4						,				down_block_types=('DownBlock2D', 'CrossAttnDownBlock2D')						,				up_block_types=('CrossAttnUpBlock2D', 'UpBlock2D')						,				cross_attention_dim=32						,				attention_head_dim=(2, 4)						,				use_linear_projection=__a						,				)
						__a			:       str					    =  PNDMScheduler(skip_prk_steps=__a							)
						torch.manual_seed(0							)
						__a			:       Union[str, Any]					    =  AutoencoderKL(
						    block_out_channels=[32, 64]						,				in_channels=3						,				out_channels=3						,				down_block_types=['DownEncoderBlock2D', 'DownEncoderBlock2D']						,				up_block_types=['UpDecoderBlock2D', 'UpDecoderBlock2D']						,				latent_channels=4						,				sample_size=128						,				)
						torch.manual_seed(0							)
						__a			:       List[str]					    =  CLIPTextConfig(
						    bos_token_id=0						,				eos_token_id=2						,				hidden_size=32						,				intermediate_size=37						,				layer_norm_eps=1E-0_5						,				num_attention_heads=4						,				num_hidden_layers=5						,				pad_token_id=1						,				vocab_size=1000						,				hidden_act='gelu'						,				projection_dim=512						,				)
						__a			:       Dict					    =  CLIPTextModel(__a							)
						__a			:       Union[str, Any]					    =  CLIPTokenizer.from_pretrained('hf-internal-testing/tiny-random-clip'							)

						__a			:       Union[str, Any]					    =  {
						    'unet': unet,
						    'scheduler': scheduler,
						    'vae': vae,
						    'text_encoder': text_encoder,
						    'tokenizer': tokenizer,
						    'safety_checker': None,
						    'feature_extractor': None,
						}
						return components




	def       __UpperCAmelCase							(   self						,				__a						,				__a=0							):

						'''simple docstring'''





						__a			:       Union[str, Any]					    =  floats_tensor((1, 3, 32, 32)						,				rng=random.Random(__a							)							).to(__a							)
						__a			:       List[Any]					    =  image.cpu().permute(0						,				2						,				3						,				1							)[0]
						__a			:       Tuple					    =  Image.fromarray(np.uinta(__a							)							).convert('RGB'							).resize((64, 64)							)
						__a			:       Tuple					    =  Image.fromarray(np.uinta(image + 4							)							).convert('RGB'							).resize((64, 64)							)
						if str(__a							).startswith('mps'							):
											__a			:       Any					    =  torch.manual_seed(__a							)
						else:
											__a			:       str					    =  torch.Generator(device=__a							).manual_seed(__a							)
						__a			:       Dict					    =  {
						    'prompt': 'A painting of a squirrel eating a burger',
						    'image': init_image,
						    'mask_image': mask_image,
						    'generator': generator,
						    'num_inference_steps': 2,
						    'guidance_scale': 6.0,
						    'output_type': 'numpy',
						}
						return inputs




	def       __UpperCAmelCase							(   self							):

						'''simple docstring'''





						__a			:       Dict					    =  'cpu'  # ensure determinism for the device-dependent torch.Generator
						__a			:       str					    =  self.get_dummy_components()
						__a			:       Union[str, Any]					    =  StableDiffusionInpaintPipeline(**__a							)
						__a			:       List[Any]					    =  sd_pipe.to(__a							)
						sd_pipe.set_progress_bar_config(disable=__a							)

						__a			:       List[Any]					    =  self.get_dummy_inputs(__a							)
						__a			:       Dict					    =  sd_pipe(**__a							).images
						__a			:       Optional[Any]					    =  image[0, -3:, -3:, -1]

						assert image.shape == (1, 64, 64, 3)
						__a			:       List[Any]					    =  np.array([0.4727, 0.5735, 0.3941, 0.5446, 0.5926, 0.4394, 0.5062, 0.4654, 0.4476]							)

						assert np.abs(image_slice.flatten() - expected_slice							).max() < 1E-2





	def       __UpperCAmelCase							(   self							):

						'''simple docstring'''





						super().test_inference_batch_single_identical(expected_max_diff=3E-3							)





@slow
@require_torch_gpu
class 							__UpperCamelCase				(		unittest.TestCase					):




	def       __UpperCAmelCase							(   self							):

						'''simple docstring'''





						super().tearDown()
						gc.collect()
						torch.cuda.empty_cache()




	def       __UpperCAmelCase							(   self							):

						'''simple docstring'''





						__a			:       List[str]					    =  load_image(
						    'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main'
						    '/sd2-inpaint/init_image.png'							)
						__a			:       List[str]					    =  load_image(
						    'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/sd2-inpaint/mask.png'							)
						__a			:       str					    =  load_numpy(
						    'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/sd2-inpaint'
						    '/yellow_cat_sitting_on_a_park_bench.npy'							)

						__a			:       Optional[int]					    =  'stabilityai/stable-diffusion-2-inpainting'
						__a			:       Optional[int]					    =  StableDiffusionInpaintPipeline.from_pretrained(__a						,				safety_checker=__a							)
						pipe.to(__a							)
						pipe.set_progress_bar_config(disable=__a							)
						pipe.enable_attention_slicing()

						__a			:       Dict					    =  'Face of a yellow cat, high resolution, sitting on a park bench'

						__a			:       Tuple					    =  torch.manual_seed(0							)
						__a			:       int					    =  pipe(
						    prompt=__a						,				image=__a						,				mask_image=__a						,				generator=__a						,				output_type='np'						,				)
						__a			:       Dict					    =  output.images[0]

						assert image.shape == (512, 512, 3)
						assert np.abs(expected_image - image							).max() < 9E-3




	def       __UpperCAmelCase							(   self							):

						'''simple docstring'''





						__a			:       Tuple					    =  load_image(
						    'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main'
						    '/sd2-inpaint/init_image.png'							)
						__a			:       int					    =  load_image(
						    'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/sd2-inpaint/mask.png'							)
						__a			:       Any					    =  load_numpy(
						    'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/sd2-inpaint'
						    '/yellow_cat_sitting_on_a_park_bench_fp16.npy'							)

						__a			:       str					    =  'stabilityai/stable-diffusion-2-inpainting'
						__a			:       List[str]					    =  StableDiffusionInpaintPipeline.from_pretrained(
						    __a						,				torch_dtype=torch.floataa						,				safety_checker=__a						,				)
						pipe.to(__a							)
						pipe.set_progress_bar_config(disable=__a							)
						pipe.enable_attention_slicing()

						__a			:       Union[str, Any]					    =  'Face of a yellow cat, high resolution, sitting on a park bench'

						__a			:       int					    =  torch.manual_seed(0							)
						__a			:       Optional[Any]					    =  pipe(
						    prompt=__a						,				image=__a						,				mask_image=__a						,				generator=__a						,				output_type='np'						,				)
						__a			:       int					    =  output.images[0]

						assert image.shape == (512, 512, 3)
						assert np.abs(expected_image - image							).max() < 5E-1





	def       __UpperCAmelCase							(   self							):

						'''simple docstring'''





						torch.cuda.empty_cache()
						torch.cuda.reset_max_memory_allocated()
						torch.cuda.reset_peak_memory_stats()

						__a			:       str					    =  load_image(
						    'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main'
						    '/sd2-inpaint/init_image.png'							)
						__a			:       List[Any]					    =  load_image(
						    'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/sd2-inpaint/mask.png'							)

						__a			:       str					    =  'stabilityai/stable-diffusion-2-inpainting'
						__a			:       Any					    =  PNDMScheduler.from_pretrained(__a						,				subfolder='scheduler'							)
						__a			:       str					    =  StableDiffusionInpaintPipeline.from_pretrained(
						    __a						,				safety_checker=__a						,				scheduler=__a						,				torch_dtype=torch.floataa						,				)
						pipe.to(__a							)
						pipe.set_progress_bar_config(disable=__a							)
						pipe.enable_attention_slicing(1							)
						pipe.enable_sequential_cpu_offload()

						__a			:       str					    =  'Face of a yellow cat, high resolution, sitting on a park bench'

						__a			:       Tuple					    =  torch.manual_seed(0							)
						__a			:       str					    =  pipe(
						    prompt=__a						,				image=__a						,				mask_image=__a						,				generator=__a						,				num_inference_steps=2						,				output_type='np'						,				)

						__a			:       List[str]					    =  torch.cuda.max_memory_allocated()
						# make sure that less than 2.65 GB is allocated
						assert mem_bytes < 2.65 * 10**9



