



'''simple docstring'''

def 	__lowerCamelCase	( )     -> str:
		for n in range(1		,     1000000    ):
				yield n * (n + 1) // 2



def 	__lowerCamelCase	( lowerCAmelCase_    )     -> int:
		_a	: Tuple								=				1
		_a	: List[Any]								=				2
		while i * i <= n:
				_a	: Union[str, Any]								=				0
				while n % i == 0:
						n //= i
						multiplicity += 1
				divisors_count *= multiplicity + 1
				i += 1
		if n > 1:
				divisors_count *= 2
		return divisors_count



def 	__lowerCamelCase	( )     -> List[str]:
		return next(i for i in triangle_number_generator() if count_divisors(lowerCAmelCase_    ) > 500    )


if __name__ == "__main__":
							print(solution())









'''simple docstring'''

import unittest

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

from diffusers import DDIMScheduler, LDMPipeline, UNetaDModel, VQModel
from diffusers.utils.testing_utils import enable_full_determinism, require_torch, slow, torch_device


enable_full_determinism()

class       __magic_name__		(       unittest.TestCase  ):







							@property
							def 				__lowercase     (				self   :			int						):
									torch.manual_seed(0						)
									_a	: int								=				UNetaDModel(
									    block_out_channels=(32, 64)      ,layers_per_block=2      ,sample_size=32      ,in_channels=3      ,out_channels=3      ,down_block_types=('DownBlock2D', 'AttnDownBlock2D')      ,up_block_types=('AttnUpBlock2D', 'UpBlock2D')      ,)
									return model







							@property
							def 				__lowercase     (				self   :			Any						):
									torch.manual_seed(0						)
									_a	: int								=				VQModel(
									    block_out_channels=[32, 64]      ,in_channels=3      ,out_channels=3      ,down_block_types=['DownEncoderBlock2D', 'DownEncoderBlock2D']      ,up_block_types=['UpDecoderBlock2D', 'UpDecoderBlock2D']      ,latent_channels=3      ,)
									return model







							@property
							def 				__lowercase     (				self   :			Union[str, Any]						):
									torch.manual_seed(0						)
									_a	: Dict								=				CLIPTextConfig(
									    bos_token_id=0      ,eos_token_id=2      ,hidden_size=32      ,intermediate_size=37      ,layer_norm_eps=1E-05      ,num_attention_heads=4      ,num_hidden_layers=5      ,pad_token_id=1      ,vocab_size=1000      ,)
									return CLIPTextModel(_UpperCAmelCase						)







							def 				__lowercase     (				self   :			Dict						):
									_a	: Union[str, Any]								=				self.dummy_uncond_unet
									_a	: Union[str, Any]								=				DDIMScheduler()
									_a	: Union[str, Any]								=				self.dummy_vq_model

									_a	: List[Any]								=				LDMPipeline(unet=_UpperCAmelCase      ,vqvae=_UpperCAmelCase      ,scheduler=_UpperCAmelCase						)
									ldm.to(_UpperCAmelCase						)
									ldm.set_progress_bar_config(disable=_UpperCAmelCase						)

									_a	: Dict								=				torch.manual_seed(0						)
									_a	: int								=				ldm(generator=_UpperCAmelCase      ,num_inference_steps=2      ,output_type='numpy'						).images

									_a	: Tuple								=				torch.manual_seed(0						)
									_a	: List[Any]								=				ldm(generator=_UpperCAmelCase      ,num_inference_steps=2      ,output_type='numpy'      ,return_dict=_UpperCAmelCase						)[0]

									_a	: Any								=				image[0, -3:, -3:, -1]
									_a	: List[Any]								=				image_from_tuple[0, -3:, -3:, -1]

									assert image.shape == (1, 64, 64, 3)
									_a	: Union[str, Any]								=				np.array([0.85_12, 0.8_18, 0.64_11, 0.68_08, 0.44_65, 0.56_18, 0.46, 0.62_31, 0.51_72]						)
									_a	: Any								=				1E-2 if torch_device != 'mps' else 3E-2

									assert np.abs(image_slice.flatten() - expected_slice						).max() < tolerance
									assert np.abs(image_from_tuple_slice.flatten() - expected_slice						).max() < tolerance

@slow
@require_torch
class       __magic_name__		(       unittest.TestCase  ):







							def 				__lowercase     (				self   :			Optional[int]						):
									_a	: Dict								=				LDMPipeline.from_pretrained('CompVis/ldm-celebahq-256'						)
									ldm.to(_UpperCAmelCase						)
									ldm.set_progress_bar_config(disable=_UpperCAmelCase						)

									_a	: str								=				torch.manual_seed(0						)
									_a	: Optional[Any]								=				ldm(generator=_UpperCAmelCase      ,num_inference_steps=5      ,output_type='numpy'						).images

									_a	: Optional[Any]								=				image[0, -3:, -3:, -1]

									assert image.shape == (1, 256, 256, 3)
									_a	: Union[str, Any]								=				np.array([0.43_99, 0.4_49_75, 0.4_68_25, 0.4_74, 0.43_59, 0.45_81, 0.4_50_95, 0.43_41, 0.44_47]						)
									_a	: List[str]								=				1E-2 if torch_device != 'mps' else 3E-2

									assert np.abs(image_slice.flatten() - expected_slice						).max() < tolerance




