




"""simple docstring"""

import math

def 		lowercase_   (		_UpperCAmelCase						):




	"""simple docstring"""






	if 1 < number < 4:
		# 2 and 3 are primes
		return True
	elif number < 2 or number % 2 == 0 or number % 3 == 0:
		# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
		return False

	# All primes number are in format of 6k +/- 1
	for i in range(5	,   int(math.sqrt(_UpperCAmelCase						) + 1						)	,   6						):
		if number % i == 0 or number % (i + 2) == 0:
			return False
	return True

def 		lowercase_   (		_UpperCAmelCase = 1000	,   _UpperCAmelCase = 1000						):




	"""simple docstring"""






	A_	:					Dict						 =		[0, 0, 0]  # length, a, b
	for a in range((a_limit * -1) + 1	,   _UpperCAmelCase						):
		for b in range(2	,   _UpperCAmelCase						):
			if is_prime(_UpperCAmelCase						):
				A_	:					int						 =		0
				A_	:					Tuple						 =		0
				while is_prime((n**2) + (a * n) + b						):
					count += 1
					n += 1
				if count > longest[0]:
					A_	:					Tuple						 =		[count, a, b]
	A_	:					List[str]						 =		longest[1] * longest[2]
	return ans


if __name__ == "__main__":
		print(solution(1000, 1000))











"""simple docstring"""

import gc
import os
import tempfile
import unittest

import torch
import torch.nn as nn
import torch.nn.functional as F
from transformers import CLIPTextConfig, CLIPTextModel, CLIPTokenizer

from diffusers import AutoencoderKL, DDIMScheduler, StableDiffusionPipeline, UNetaDConditionModel
from diffusers.loaders import AttnProcsLayers, LoraLoaderMixin
from diffusers.models.attention_processor import (
    Attention,
    AttnProcessor,
    AttnProcessor2_0,
    LoRAAttnProcessor,
    LoRAAttnProcessor2_0,
    LoRAXFormersAttnProcessor,
    XFormersAttnProcessor,
)
from diffusers.utils import TEXT_ENCODER_ATTN_MODULE, floats_tensor, torch_device

def 		lowercase_   (		_UpperCAmelCase						):




	"""simple docstring"""






	A_	:					Any						 =		{}
	for name in unet.attn_processors.keys():
		A_	:					Dict						 =		None if name.endswith('''attn1.processor'''						) else unet.config.cross_attention_dim
		if name.startswith('''mid_block'''						):
			A_	:					List[str]						 =		unet.config.block_out_channels[-1]
		elif name.startswith('''up_blocks'''						):
			A_	:					List[str]						 =		int(name[len('''up_blocks.'''						)]						)
			A_	:					int						 =		list(reversed(unet.config.block_out_channels						)						)[block_id]
		elif name.startswith('''down_blocks'''						):
			A_	:					int						 =		int(name[len('''down_blocks.'''						)]						)
			A_	:					str						 =		unet.config.block_out_channels[block_id]
		A_	:					int						 =		(
		    LoRAAttnProcessor2_0 if hasattr(_UpperCAmelCase	,   '''scaled_dot_product_attention'''						) else LoRAAttnProcessor
		)
		A_	:					Optional[Any]						 =		lora_attn_processor_class(
		    hidden_size=_UpperCAmelCase	,   cross_attention_dim=_UpperCAmelCase						)
	A_	:					Dict						 =		AttnProcsLayers(_UpperCAmelCase						)
	return lora_attn_procs, unet_lora_layers

def 		lowercase_   (		_UpperCAmelCase						):




	"""simple docstring"""






	A_	:					Union[str, Any]						 =		{}
	A_	:					List[str]						 =		(
	    LoRAAttnProcessor2_0 if hasattr(_UpperCAmelCase	,   '''scaled_dot_product_attention'''						) else LoRAAttnProcessor
	)
	for name, module in text_encoder.named_modules():
		if name.endswith(_UpperCAmelCase						):
			A_	:					Optional[int]						 =		lora_attn_processor_class(
			    hidden_size=module.out_proj.out_features	,   cross_attention_dim=_UpperCAmelCase						)
	return text_lora_attn_procs

def 		lowercase_   (		_UpperCAmelCase						):




	"""simple docstring"""






	A_	:					Optional[Any]						 =		create_text_encoder_lora_attn_procs(_UpperCAmelCase						)
	A_	:					List[str]						 =		AttnProcsLayers(_UpperCAmelCase						)
	return text_encoder_lora_layers

def 		lowercase_   (		_UpperCAmelCase	,   _UpperCAmelCase=False						):




	"""simple docstring"""






	for _, attn_proc in text_lora_attn_procs.items():
		# set up.weights
		for layer_name, layer_module in attn_proc.named_modules():
			if layer_name.endswith('''_lora'''						):
				A_	:					List[Any]						 =		(
				    torch.randn_like(layer_module.up.weight						)
				    if randn_weight
				    else torch.zeros_like(layer_module.up.weight						)
				)
				A_	:					Tuple						 =		torch.nn.Parameter(_UpperCAmelCase						)

class 							lowercase   (     unittest.TestCase):







				def        a_	(				self :       List[Any]							):



					"""simple docstring"""

					torch.manual_seed(0							)
					A_	:					List[str]						 =		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   ,  )
					A_	:					Optional[int]						 =		DDIMScheduler(
					    beta_start=0.00085   ,  beta_end=0.012   ,  beta_schedule='''scaled_linear'''   ,  clip_sample=_lowerCamelCase   ,  set_alpha_to_one=_lowerCamelCase   ,  steps_offset=1   ,  )
					torch.manual_seed(0							)
					A_	:					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   ,  )
					A_	:					Union[str, Any]						 =		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=10_00   ,  )
					A_	:					List[Any]						 =		CLIPTextModel(_lowerCamelCase							)
					A_	:					str						 =		CLIPTokenizer.from_pretrained('''hf-internal-testing/tiny-random-clip'''							)

					A_ ,			A_	:					Any						 =		create_unet_lora_layers(_lowerCamelCase							)
					A_	:					Tuple						 =		create_text_encoder_lora_layers(_lowerCamelCase							)

					A_	:					Any						 =		{
					    '''unet''': unet,
					    '''scheduler''': scheduler,
					    '''vae''': vae,
					    '''text_encoder''': text_encoder,
					    '''tokenizer''': tokenizer,
					    '''safety_checker''': None,
					    '''feature_extractor''': None,
					}
					A_	:					Union[str, Any]						 =		{
					    '''unet_lora_layers''': unet_lora_layers,
					    '''text_encoder_lora_layers''': text_encoder_lora_layers,
					    '''unet_lora_attn_procs''': unet_lora_attn_procs,
					}
					return pipeline_components, lora_components







				def        a_	(				self :       str							):



					"""simple docstring"""

					A_	:					Optional[int]						 =		1
					A_	:					Tuple						 =		10
					A_	:					int						 =		4
					A_	:					List[Any]						 =		(32, 32)

					A_	:					str						 =		torch.manual_seed(0							)
					A_	:					Dict						 =		floats_tensor((batch_size, num_channels) + sizes							)
					A_	:					List[str]						 =		torch.randint(1   ,  _lowerCamelCase   ,  size=(batch_size, sequence_length)   ,  generator=_lowerCamelCase							)

					A_	:					int						 =		{
					    '''prompt''': '''A painting of a squirrel eating a burger''',
					    '''generator''': generator,
					    '''num_inference_steps''': 2,
					    '''guidance_scale''': 6.0,
					    '''output_type''': '''numpy''',
					}

					return noise, input_ids, pipeline_inputs

					# copied from: https://colab.research.google.com/gist/sayakpaul/df2ef6e1ae6d8c10a49d859883b10860/scratchpad.ipynb







				def        a_	(				self :       str							):



					"""simple docstring"""

					A_	:					Union[str, Any]						 =		77

					A_	:					str						 =		torch.randint(2   ,  56   ,  size=(1, max_seq_length)   ,  generator=torch.manual_seed(0							)							)

					A_	:					Optional[Any]						 =		{}
					A_	:					int						 =		inputs
					return prepared_inputs







				def        a_	(				self :       Optional[int]   ,  _lowerCamelCase :       List[Any]							):



					"""simple docstring"""

					A_ ,			A_	:					List[str]						 =		self.get_dummy_components()
					LoraLoaderMixin.save_lora_weights(
					    save_directory=_lowerCamelCase   ,  unet_lora_layers=lora_components['''unet_lora_layers''']   ,  text_encoder_lora_layers=lora_components['''text_encoder_lora_layers''']   ,  )
					self.assertTrue(os.path.isfile(os.path.join(_lowerCamelCase   ,  '''pytorch_lora_weights.bin'''							)							)							)







				def        a_	(				self :       Any							):



					"""simple docstring"""

					A_ ,			A_	:					Optional[Any]						 =		self.get_dummy_components()
					A_	:					List[str]						 =		StableDiffusionPipeline(**_lowerCamelCase							)
					A_	:					List[str]						 =		sd_pipe.to(_lowerCamelCase							)
					sd_pipe.set_progress_bar_config(disable=_lowerCamelCase							)

					A_ ,			A_ ,			A_	:					str						 =		self.get_dummy_inputs()

					A_	:					Optional[int]						 =		sd_pipe(**_lowerCamelCase							).images
					A_	:					str						 =		original_images[0, -3:, -3:, -1]

					with tempfile.TemporaryDirectory() as tmpdirname:
						LoraLoaderMixin.save_lora_weights(
						    save_directory=_lowerCamelCase   ,  unet_lora_layers=lora_components['''unet_lora_layers''']   ,  text_encoder_lora_layers=lora_components['''text_encoder_lora_layers''']   ,  )
						self.assertTrue(os.path.isfile(os.path.join(_lowerCamelCase   ,  '''pytorch_lora_weights.bin'''							)							)							)
						sd_pipe.load_lora_weights(_lowerCamelCase							)

					A_	:					List[Any]						 =		sd_pipe(**_lowerCamelCase							).images
					A_	:					str						 =		lora_images[0, -3:, -3:, -1]

					# Outputs shouldn't match.
					self.assertFalse(torch.allclose(torch.from_numpy(_lowerCamelCase							)   ,  torch.from_numpy(_lowerCamelCase							)							)							)







				def        a_	(				self :       Optional[int]							):



					"""simple docstring"""

					A_ ,			A_	:					List[Any]						 =		self.get_dummy_components()
					A_	:					str						 =		StableDiffusionPipeline(**_lowerCamelCase							)
					A_	:					Any						 =		sd_pipe.to(_lowerCamelCase							)
					sd_pipe.set_progress_bar_config(disable=_lowerCamelCase							)

					A_ ,			A_ ,			A_	:					List[str]						 =		self.get_dummy_inputs()

					A_	:					Union[str, Any]						 =		sd_pipe(**_lowerCamelCase							).images
					A_	:					int						 =		original_images[0, -3:, -3:, -1]

					with tempfile.TemporaryDirectory() as tmpdirname:
						LoraLoaderMixin.save_lora_weights(
						    save_directory=_lowerCamelCase   ,  unet_lora_layers=lora_components['''unet_lora_layers''']   ,  text_encoder_lora_layers=lora_components['''text_encoder_lora_layers''']   ,  safe_serialization=_lowerCamelCase   ,  )
						self.assertTrue(os.path.isfile(os.path.join(_lowerCamelCase   ,  '''pytorch_lora_weights.safetensors'''							)							)							)
						sd_pipe.load_lora_weights(_lowerCamelCase							)

					A_	:					Union[str, Any]						 =		sd_pipe(**_lowerCamelCase							).images
					A_	:					Dict						 =		lora_images[0, -3:, -3:, -1]

					# Outputs shouldn't match.
					self.assertFalse(torch.allclose(torch.from_numpy(_lowerCamelCase							)   ,  torch.from_numpy(_lowerCamelCase							)							)							)







				def        a_	(				self :       Optional[int]							):



					"""simple docstring"""

					A_ ,			A_	:					List[Any]						 =		self.get_dummy_components()
					A_	:					Any						 =		lora_components['''unet_lora_attn_procs''']
					A_	:					Any						 =		StableDiffusionPipeline(**_lowerCamelCase							)
					A_	:					Tuple						 =		sd_pipe.to(_lowerCamelCase							)
					sd_pipe.set_progress_bar_config(disable=_lowerCamelCase							)

					A_ ,			A_ ,			A_	:					Tuple						 =		self.get_dummy_inputs()

					A_	:					Tuple						 =		sd_pipe(**_lowerCamelCase							).images
					A_	:					Optional[Any]						 =		original_images[0, -3:, -3:, -1]

					with tempfile.TemporaryDirectory() as tmpdirname:
						A_	:					Tuple						 =		sd_pipe.unet
						unet.set_attn_processor(_lowerCamelCase							)
						unet.save_attn_procs(_lowerCamelCase							)
						self.assertTrue(os.path.isfile(os.path.join(_lowerCamelCase   ,  '''pytorch_lora_weights.bin'''							)							)							)
						sd_pipe.load_lora_weights(_lowerCamelCase							)

					A_	:					Any						 =		sd_pipe(**_lowerCamelCase							).images
					A_	:					Optional[int]						 =		lora_images[0, -3:, -3:, -1]

					# Outputs shouldn't match.
					self.assertFalse(torch.allclose(torch.from_numpy(_lowerCamelCase							)   ,  torch.from_numpy(_lowerCamelCase							)							)							)







				def        a_	(				self :       Tuple							):



					"""simple docstring"""

					A_ ,			A_	:					List[str]						 =		self.get_dummy_components()
					A_	:					Dict						 =		StableDiffusionPipeline(**_lowerCamelCase							)

					A_	:					Any						 =		self.get_dummy_tokens()

					# inference without lora
					A_	:					str						 =		pipe.text_encoder(**_lowerCamelCase							)[0]
					assert outputs_without_lora.shape == (1, 77, 32)

					# create lora_attn_procs with zeroed out up.weights
					A_	:					str						 =		create_text_encoder_lora_attn_procs(pipe.text_encoder							)
					set_lora_up_weights(_lowerCamelCase   ,  randn_weight=_lowerCamelCase							)

					# monkey patch
					pipe._modify_text_encoder(_lowerCamelCase							)

					# verify that it's okay to release the text_attn_procs which holds the LoRAAttnProcessor.
					del text_attn_procs
					gc.collect()

					# inference with lora
					A_	:					List[str]						 =		pipe.text_encoder(**_lowerCamelCase							)[0]
					assert outputs_with_lora.shape == (1, 77, 32)

					assert torch.allclose(
					    _lowerCamelCase   ,  _lowerCamelCase							), "lora_up_weight are all zero, so the lora outputs should be the same to without lora outputs"

					# create lora_attn_procs with randn up.weights
					A_	:					Tuple						 =		create_text_encoder_lora_attn_procs(pipe.text_encoder							)
					set_lora_up_weights(_lowerCamelCase   ,  randn_weight=_lowerCamelCase							)

					# monkey patch
					pipe._modify_text_encoder(_lowerCamelCase							)

					# verify that it's okay to release the text_attn_procs which holds the LoRAAttnProcessor.
					del text_attn_procs
					gc.collect()

					# inference with lora
					A_	:					str						 =		pipe.text_encoder(**_lowerCamelCase							)[0]
					assert outputs_with_lora.shape == (1, 77, 32)

					assert not torch.allclose(
					    _lowerCamelCase   ,  _lowerCamelCase							), "lora_up_weight are not zero, so the lora outputs should be different to without lora outputs"







				def        a_	(				self :       Optional[int]							):



					"""simple docstring"""

					A_ ,			A_	:					List[Any]						 =		self.get_dummy_components()
					A_	:					Optional[int]						 =		StableDiffusionPipeline(**_lowerCamelCase							)

					A_	:					List[Any]						 =		self.get_dummy_tokens()

					# inference without lora
					A_	:					Tuple						 =		pipe.text_encoder(**_lowerCamelCase							)[0]
					assert outputs_without_lora.shape == (1, 77, 32)

					# create lora_attn_procs with randn up.weights
					A_	:					List[Any]						 =		create_text_encoder_lora_attn_procs(pipe.text_encoder							)
					set_lora_up_weights(_lowerCamelCase   ,  randn_weight=_lowerCamelCase							)

					# monkey patch
					pipe._modify_text_encoder(_lowerCamelCase							)

					# verify that it's okay to release the text_attn_procs which holds the LoRAAttnProcessor.
					del text_attn_procs
					gc.collect()

					# inference with lora
					A_	:					List[Any]						 =		pipe.text_encoder(**_lowerCamelCase							)[0]
					assert outputs_with_lora.shape == (1, 77, 32)

					assert not torch.allclose(
					    _lowerCamelCase   ,  _lowerCamelCase							), "lora outputs should be different to without lora outputs"

					# remove monkey patch
					pipe._remove_text_encoder_monkey_patch()

					# inference with removed lora
					A_	:					Optional[int]						 =		pipe.text_encoder(**_lowerCamelCase							)[0]
					assert outputs_without_lora_removed.shape == (1, 77, 32)

					assert torch.allclose(
					    _lowerCamelCase   ,  _lowerCamelCase							), "remove lora monkey patch should restore the original outputs"







				def        a_	(				self :       Tuple							):



					"""simple docstring"""

					A_ ,			A_	:					Dict						 =		self.get_dummy_components()
					A_	:					str						 =		StableDiffusionPipeline(**_lowerCamelCase							)
					A_	:					Dict						 =		sd_pipe.to(_lowerCamelCase							)
					sd_pipe.set_progress_bar_config(disable=_lowerCamelCase							)

					A_ ,			A_ ,			A_	:					Tuple						 =		self.get_dummy_inputs()

					with tempfile.TemporaryDirectory() as tmpdirname:
						LoraLoaderMixin.save_lora_weights(
						    save_directory=_lowerCamelCase   ,  unet_lora_layers=lora_components['''unet_lora_layers''']   ,  text_encoder_lora_layers=lora_components['''text_encoder_lora_layers''']   ,  )
						self.assertTrue(os.path.isfile(os.path.join(_lowerCamelCase   ,  '''pytorch_lora_weights.bin'''							)							)							)
						sd_pipe.load_lora_weights(_lowerCamelCase							)

					A_	:					Dict						 =		sd_pipe(**_lowerCamelCase							).images
					A_	:					Union[str, Any]						 =		lora_images[0, -3:, -3:, -1]

					A_	:					int						 =		sd_pipe(**_lowerCamelCase   ,  cross_attention_kwargs={'''scale''': 0.5}							).images
					A_	:					int						 =		lora_images_with_scale[0, -3:, -3:, -1]

					# Outputs shouldn't match.
					self.assertFalse(
					    torch.allclose(torch.from_numpy(_lowerCamelCase							)   ,  torch.from_numpy(_lowerCamelCase							)							)							)







				def        a_	(				self :       Tuple							):



					"""simple docstring"""

					with tempfile.TemporaryDirectory() as tmpdirname:
						self.create_lora_weight_file(_lowerCamelCase							)

						A_ ,			A_	:					str						 =		self.get_dummy_components()
						A_	:					Optional[Any]						 =		StableDiffusionPipeline(**_lowerCamelCase							)
						A_	:					List[Any]						 =		sd_pipe.to(_lowerCamelCase							)
						sd_pipe.set_progress_bar_config(disable=_lowerCamelCase							)

						# check if vanilla attention processors are used
						for _, module in sd_pipe.unet.named_modules():
							if isinstance(_lowerCamelCase   ,  _lowerCamelCase							):
								self.assertIsInstance(module.processor   ,  (AttnProcessor, AttnProcessor2_0)							)

            # load LoRA weight file
						sd_pipe.load_lora_weights(_lowerCamelCase							)

						# check if lora attention processors are used
						for _, module in sd_pipe.unet.named_modules():
							if isinstance(_lowerCamelCase   ,  _lowerCamelCase							):
								A_	:					Any						 =		(
								    LoRAAttnProcessor2_0 if hasattr(_lowerCamelCase   ,  '''scaled_dot_product_attention'''							) else LoRAAttnProcessor
								)
								self.assertIsInstance(module.processor   ,  _lowerCamelCase							)







				@unittest.skipIf(torch_device != '''cuda'''   ,  '''This test is supposed to run on GPU'''							)
				def        a_	(				self :       Optional[Any]							):



					"""simple docstring"""

					with tempfile.TemporaryDirectory() as tmpdirname:
						self.create_lora_weight_file(_lowerCamelCase							)

						A_ ,			A_	:					Tuple						 =		self.get_dummy_components()
						A_	:					Optional[int]						 =		StableDiffusionPipeline(**_lowerCamelCase							)
						A_	:					Any						 =		sd_pipe.to(_lowerCamelCase							)
						sd_pipe.set_progress_bar_config(disable=_lowerCamelCase							)

						# enable XFormers
						sd_pipe.enable_xformers_memory_efficient_attention()

						# check if xFormers attention processors are used
						for _, module in sd_pipe.unet.named_modules():
							if isinstance(_lowerCamelCase   ,  _lowerCamelCase							):
								self.assertIsInstance(module.processor   ,  _lowerCamelCase							)

            # load LoRA weight file
						sd_pipe.load_lora_weights(_lowerCamelCase							)

						# check if lora attention processors are used
						for _, module in sd_pipe.unet.named_modules():
							if isinstance(_lowerCamelCase   ,  _lowerCamelCase							):
								self.assertIsInstance(module.processor   ,  _lowerCamelCase							)







				@unittest.skipIf(torch_device != '''cuda'''   ,  '''This test is supposed to run on GPU'''							)
				def        a_	(				self :       Optional[Any]							):



					"""simple docstring"""

					A_ ,			A_	:					Any						 =		self.get_dummy_components()
					A_	:					Union[str, Any]						 =		StableDiffusionPipeline(**_lowerCamelCase							)
					A_	:					Optional[int]						 =		sd_pipe.to(_lowerCamelCase							)
					sd_pipe.set_progress_bar_config(disable=_lowerCamelCase							)

					A_ ,			A_ ,			A_	:					int						 =		self.get_dummy_inputs()

					# enable XFormers
					sd_pipe.enable_xformers_memory_efficient_attention()

					A_	:					str						 =		sd_pipe(**_lowerCamelCase							).images
					A_	:					Tuple						 =		original_images[0, -3:, -3:, -1]

					with tempfile.TemporaryDirectory() as tmpdirname:
						LoraLoaderMixin.save_lora_weights(
						    save_directory=_lowerCamelCase   ,  unet_lora_layers=lora_components['''unet_lora_layers''']   ,  text_encoder_lora_layers=lora_components['''text_encoder_lora_layers''']   ,  )
						self.assertTrue(os.path.isfile(os.path.join(_lowerCamelCase   ,  '''pytorch_lora_weights.bin'''							)							)							)
						sd_pipe.load_lora_weights(_lowerCamelCase							)

					A_	:					List[Any]						 =		sd_pipe(**_lowerCamelCase							).images
					A_	:					int						 =		lora_images[0, -3:, -3:, -1]

					# Outputs shouldn't match.
					self.assertFalse(torch.allclose(torch.from_numpy(_lowerCamelCase							)   ,  torch.from_numpy(_lowerCamelCase							)							)							)





