


'''simple docstring'''




from math import sqrt

def 			__UpperCamelCase    (    _A    :				int = 1_00_00_00				)    ->      int:




	"""simple docstring"""





	lowerCAmelCase					:    int      							= 0
	lowerCAmelCase					:    int      							= 0
	lowerCAmelCase					:    int

	while num_cuboids <= limit:
		max_cuboid_size += 1
		for sum_shortest_sides in range(2					,   2 * max_cuboid_size + 1				):
			if sqrt(sum_shortest_sides**2 + max_cuboid_size**2				).is_integer():
				num_cuboids += (
				    min(_A					,   sum_shortest_sides // 2				)
				    - max(1					,   sum_shortest_sides - max_cuboid_size				)
				    + 1
				)

	return max_cuboid_size


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




'''simple docstring'''




import gc
import unittest

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

from diffusers import AutoencoderKL, DDIMScheduler, LDMTextToImagePipeline, UNetaDConditionModel
from diffusers.utils.testing_utils import (
    enable_full_determinism,
    load_numpy,
    nightly,
    require_torch_gpu,
    slow,
    torch_device,
)

from ..pipeline_params import TEXT_TO_IMAGE_BATCH_PARAMS, TEXT_TO_IMAGE_PARAMS
from ..test_pipelines_common import PipelineTesterMixin


enable_full_determinism()



class  lowerCAmelCase				(				a      ,				unittest.TestCase							):
	_lowerCamelCase   :					List[Any]			      = LDMTextToImagePipeline
	_lowerCamelCase   :					Optional[Any]			      = TEXT_TO_IMAGE_PARAMS - {
	    """negative_prompt""",
	    """negative_prompt_embeds""",
	    """cross_attention_kwargs""",
	    """prompt_embeds""",
	}
	_lowerCamelCase   :					List[str]			      = PipelineTesterMixin.required_optional_params - {
	    """num_images_per_prompt""",
	    """callback""",
	    """callback_steps""",
	}
	_lowerCamelCase   :					Union[str, Any]			      = TEXT_TO_IMAGE_BATCH_PARAMS
	_lowerCamelCase   :					Optional[int]			      = False



	def 				lowercase     (					self    ):
		torch.manual_seed(0    )
		lowerCAmelCase					:    Dict      							= UNetaDConditionModel(
		    block_out_channels=(32, 64) ,					layers_per_block=2 ,					sample_size=32 ,					in_channels=4 ,					out_channels=4 ,					down_block_types=('DownBlock2D', 'CrossAttnDownBlock2D') ,					up_block_types=('CrossAttnUpBlock2D', 'UpBlock2D') ,					cross_attention_dim=32 ,					)
		lowerCAmelCase					:    int      							= DDIMScheduler(
		    beta_start=0.0_0_0_8_5 ,					beta_end=0.0_1_2 ,					beta_schedule='scaled_linear' ,					clip_sample=snake_case__ ,					set_alpha_to_one=snake_case__ ,					)
		torch.manual_seed(0    )
		lowerCAmelCase					:    str      							= 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 ,					)
		torch.manual_seed(0    )
		lowerCAmelCase					:    Any      							= 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 ,					)
		lowerCAmelCase					:    str      							= CLIPTextModel(snake_case__    )
		lowerCAmelCase					:    str      							= CLIPTokenizer.from_pretrained('hf-internal-testing/tiny-random-clip'    )

		lowerCAmelCase					:    List[Any]      							= {
		    'unet': unet,
		    'scheduler': scheduler,
		    'vqvae': vae,
		    'bert': text_encoder,
		    'tokenizer': tokenizer,
		}
		return components



	def 				lowercase     (					self ,					snake_case__ ,					snake_case__=0    ):
		if str(snake_case__    ).startswith('mps'    ):
			lowerCAmelCase					:    Optional[int]      							= torch.manual_seed(snake_case__    )
		else:
			lowerCAmelCase					:    str      							= torch.Generator(device=snake_case__    ).manual_seed(snake_case__    )
		lowerCAmelCase					:    Tuple      							= {
		    'prompt': 'A painting of a squirrel eating a burger',
		    'generator': generator,
		    'num_inference_steps': 2,
		    'guidance_scale': 6.0,
		    'output_type': 'numpy',
		}
		return inputs



	def 				lowercase     (					self    ):
		lowerCAmelCase					:    List[str]      							= 'cpu'  # ensure determinism for the device-dependent torch.Generator

		lowerCAmelCase					:    Optional[Any]      							= self.get_dummy_components()
		lowerCAmelCase					:    Optional[Any]      							= LDMTextToImagePipeline(**snake_case__    )
		pipe.to(snake_case__    )
		pipe.set_progress_bar_config(disable=snake_case__    )

		lowerCAmelCase					:    Tuple      							= self.get_dummy_inputs(snake_case__    )
		lowerCAmelCase					:    Union[str, Any]      							= pipe(**snake_case__    ).images
		lowerCAmelCase					:    str      							= image[0, -3:, -3:, -1]

		assert image.shape == (1, 16, 16, 3)
		lowerCAmelCase					:    List[Any]      							= np.array([0.6_1_0_1, 0.6_1_5_6, 0.5_6_2_2, 0.4_8_9_5, 0.6_6_6_1, 0.3_8_0_4, 0.5_7_4_8, 0.6_1_3_6, 0.5_0_1_4]    )

		assert np.abs(image_slice.flatten() - expected_slice    ).max() < 1e-3



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



	def 				lowercase     (					self    ):
		super().tearDown()
		gc.collect()
		torch.cuda.empty_cache()



	def 				lowercase     (					self ,					snake_case__ ,					snake_case__=torch.floataa ,					snake_case__=0    ):
		lowerCAmelCase					:    List[str]      							= torch.manual_seed(snake_case__    )
		lowerCAmelCase					:    int      							= np.random.RandomState(snake_case__    ).standard_normal((1, 4, 32, 32)    )
		lowerCAmelCase					:    Optional[Any]      							= torch.from_numpy(snake_case__    ).to(device=snake_case__ ,					dtype=snake_case__    )
		lowerCAmelCase					:    List[str]      							= {
		    'prompt': 'A painting of a squirrel eating a burger',
		    'latents': latents,
		    'generator': generator,
		    'num_inference_steps': 3,
		    'guidance_scale': 6.0,
		    'output_type': 'numpy',
		}
		return inputs



	def 				lowercase     (					self    ):
		lowerCAmelCase					:    Tuple      							= LDMTextToImagePipeline.from_pretrained('CompVis/ldm-text2im-large-256'    ).to(snake_case__    )
		pipe.set_progress_bar_config(disable=snake_case__    )

		lowerCAmelCase					:    Optional[Any]      							= self.get_inputs(snake_case__    )
		lowerCAmelCase					:    List[Any]      							= pipe(**snake_case__    ).images
		lowerCAmelCase					:    str      							= image[0, -3:, -3:, -1].flatten()

		assert image.shape == (1, 256, 256, 3)
		lowerCAmelCase					:    Tuple      							= np.array([0.5_1_8_2_5, 0.5_2_8_5_0, 0.5_2_5_4_3, 0.5_4_2_5_8, 0.5_2_3_0_4, 0.5_2_5_6_9, 0.5_4_3_6_3, 0.5_5_2_7_6, 0.5_6_8_7_8]    )
		lowerCAmelCase					:    int      							= np.abs(expected_slice - image_slice    ).max()
		assert max_diff < 1e-3



@nightly
@require_torch_gpu
class  lowerCAmelCase				(				unittest.TestCase							):



	def 				lowercase     (					self    ):
		super().tearDown()
		gc.collect()
		torch.cuda.empty_cache()



	def 				lowercase     (					self ,					snake_case__ ,					snake_case__=torch.floataa ,					snake_case__=0    ):
		lowerCAmelCase					:    List[str]      							= torch.manual_seed(snake_case__    )
		lowerCAmelCase					:    Any      							= np.random.RandomState(snake_case__    ).standard_normal((1, 4, 32, 32)    )
		lowerCAmelCase					:    List[Any]      							= torch.from_numpy(snake_case__    ).to(device=snake_case__ ,					dtype=snake_case__    )
		lowerCAmelCase					:    List[str]      							= {
		    'prompt': 'A painting of a squirrel eating a burger',
		    'latents': latents,
		    'generator': generator,
		    'num_inference_steps': 50,
		    'guidance_scale': 6.0,
		    'output_type': 'numpy',
		}
		return inputs



	def 				lowercase     (					self    ):
		lowerCAmelCase					:    Optional[int]      							= LDMTextToImagePipeline.from_pretrained('CompVis/ldm-text2im-large-256'    ).to(snake_case__    )
		pipe.set_progress_bar_config(disable=snake_case__    )

		lowerCAmelCase					:    int      							= self.get_inputs(snake_case__    )
		lowerCAmelCase					:    Optional[int]      							= pipe(**snake_case__    ).images[0]

		lowerCAmelCase					:    Optional[int]      							= load_numpy(
		    'https://huggingface.co/datasets/diffusers/test-arrays/resolve/main/ldm_text2img/ldm_large_256_ddim.npy'    )
		lowerCAmelCase					:    List[str]      							= np.abs(expected_image - image    ).max()
		assert max_diff < 1e-3
