


'''simple docstring'''

import math



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					int )		->       bool:





   '''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 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					int = 10_00     ,		_UpperCamelCase   :					int = 10_00 )		->       int:





   '''simple docstring'''







   UpperCamelCase__			    =    [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 ):
            UpperCamelCase__			    =    0
            UpperCamelCase__			    =    0
            while is_prime((n**2) + (a * n) + b ):
               count += 1
               n += 1
            if count > longest[0]:
               UpperCamelCase__			    =    [count, a, b]
   UpperCamelCase__			    =    longest[1] * longest[2]
   return ans


if __name__ == "__main__":
       print(solution(1_000, 1_000))



'''simple docstring'''

import random
import unittest

import numpy as np
import torch
from PIL import Image
from torch import nn
from transformers import (
    CLIPImageProcessor,
    CLIPTextConfig,
    CLIPTextModelWithProjection,
    CLIPTokenizer,
    CLIPVisionConfig,
    CLIPVisionModelWithProjection,
)

from diffusers import KandinskyVaaPriorEmbaEmbPipeline, PriorTransformer, UnCLIPScheduler
from diffusers.utils import floats_tensor, torch_device
from diffusers.utils.testing_utils import enable_full_determinism, skip_mps

from ..test_pipelines_common import PipelineTesterMixin


enable_full_determinism()







class 			UpperCAmelCase			(							SCREAMING_SNAKE_CASE__		,      unittest.TestCase):
 _lowerCamelCase			:       List[Any]            =       KandinskyVaaPriorEmbaEmbPipeline
 _lowerCamelCase			:       Tuple            =       ['prompt', 'image']
 _lowerCamelCase			:       List[str]            =       ['prompt', 'image']
 _lowerCamelCase			:       List[str]            =       [
     'num_images_per_prompt',
     'strength',
     'generator',
     'num_inference_steps',
     'latents',
     'negative_prompt',
     'guidance_scale',
     'output_type',
     'return_dict',
 ]
 _lowerCamelCase			:       List[str]            =       False

 @property
 def 		lowercase_    (			self			:						int       ):





    """simple docstring"""



    return 32

 @property
 def 		lowercase_    (			self			:						Union[str, Any]       ):





    """simple docstring"""



    return 32

 @property
 def 		lowercase_    (			self			:						Any       ):





    """simple docstring"""



    return self.time_input_dim

 @property
 def 		lowercase_    (			self			:						Dict       ):





    """simple docstring"""



    return self.time_input_dim * 4

 @property
 def 		lowercase_    (			self			:						str       ):





    """simple docstring"""



    return 100

 @property
 def 		lowercase_    (			self			:						Any       ):





    """simple docstring"""



    UpperCamelCase__			    =    CLIPTokenizer.from_pretrained("hf-internal-testing/tiny-random-clip"       )
    return tokenizer

 @property
 def 		lowercase_    (			self			:						Optional[int]       ):





    """simple docstring"""



    torch.manual_seed(0       )
    UpperCamelCase__			    =    CLIPTextConfig(
        bos_token_id=0,       eos_token_id=2,       hidden_size=self.text_embedder_hidden_size,       projection_dim=self.text_embedder_hidden_size,       intermediate_size=37,       layer_norm_eps=1e-0_5,       num_attention_heads=4,       num_hidden_layers=5,       pad_token_id=1,       vocab_size=1000,       )
    return CLIPTextModelWithProjection(a_       )

 @property
 def 		lowercase_    (			self			:						str       ):





    """simple docstring"""



    torch.manual_seed(0       )

    UpperCamelCase__			    =    {
        "num_attention_heads": 2,
        "attention_head_dim": 12,
        "embedding_dim": self.text_embedder_hidden_size,
        "num_layers": 1,
    }

    UpperCamelCase__			    =    PriorTransformer(**a_       )
    # clip_std and clip_mean is initialized to be 0 so PriorTransformer.post_process_latents will always return 0 - set clip_std to be 1 so it won't return 0
    UpperCamelCase__			    =    nn.Parameter(torch.ones(model.clip_std.shape       )       )
    return model

 @property
 def 		lowercase_    (			self			:						Any       ):





    """simple docstring"""



    torch.manual_seed(0       )
    UpperCamelCase__			    =    CLIPVisionConfig(
        hidden_size=self.text_embedder_hidden_size,       image_size=224,       projection_dim=self.text_embedder_hidden_size,       intermediate_size=37,       num_attention_heads=4,       num_channels=3,       num_hidden_layers=5,       patch_size=14,       )

    UpperCamelCase__			    =    CLIPVisionModelWithProjection(a_       )
    return model

 @property
 def 		lowercase_    (			self			:						Dict       ):





    """simple docstring"""



    UpperCamelCase__			    =    CLIPImageProcessor(
        crop_size=224,       do_center_crop=a_,       do_normalize=a_,       do_resize=a_,       image_mean=[0.48_145_466, 0.4_578_275, 0.40_821_073],       image_std=[0.26_862_954, 0.26_130_258, 0.27_577_711],       resample=3,       size=224,       )

    return image_processor

 def 		lowercase_    (			self			:						Optional[int]       ):





    """simple docstring"""



    UpperCamelCase__			    =    self.dummy_prior
    UpperCamelCase__			    =    self.dummy_image_encoder
    UpperCamelCase__			    =    self.dummy_text_encoder
    UpperCamelCase__			    =    self.dummy_tokenizer
    UpperCamelCase__			    =    self.dummy_image_processor

    UpperCamelCase__			    =    UnCLIPScheduler(
        variance_type="fixed_small_log",       prediction_type="sample",       num_train_timesteps=1000,       clip_sample=a_,       clip_sample_range=10.0,       )

    UpperCamelCase__			    =    {
        "prior": prior,
        "image_encoder": image_encoder,
        "text_encoder": text_encoder,
        "tokenizer": tokenizer,
        "scheduler": scheduler,
        "image_processor": image_processor,
    }

    return components

 def 		lowercase_    (			self			:						Union[str, Any],       a_			:						List[str],       a_			:						Union[str, Any]=0       ):





    """simple docstring"""



    if str(a_       ).startswith("mps"       ):
       UpperCamelCase__			    =    torch.manual_seed(a_       )
    else:
       UpperCamelCase__			    =    torch.Generator(device=a_       ).manual_seed(a_       )

    UpperCamelCase__			    =    floats_tensor((1, 3, 64, 64),       rng=random.Random(a_       )       ).to(a_       )
    UpperCamelCase__			    =    image.cpu().permute(0,       2,       3,       1       )[0]
    UpperCamelCase__			    =    Image.fromarray(np.uinta(a_       )       ).convert("RGB"       ).resize((256, 256)       )

    UpperCamelCase__			    =    {
        "prompt": "horse",
        "image": init_image,
        "strength": 0.5,
        "generator": generator,
        "guidance_scale": 4.0,
        "num_inference_steps": 2,
        "output_type": "np",
    }
    return inputs

 def 		lowercase_    (			self			:						Union[str, Any]       ):





    """simple docstring"""



    UpperCamelCase__			    =    "cpu"

    UpperCamelCase__			    =    self.get_dummy_components()

    UpperCamelCase__			    =    self.pipeline_class(**a_       )
    UpperCamelCase__			    =    pipe.to(a_       )

    pipe.set_progress_bar_config(disable=a_       )

    UpperCamelCase__			    =    pipe(**self.get_dummy_inputs(a_       )       )
    UpperCamelCase__			    =    output.image_embeds

    UpperCamelCase__			    =    pipe(
        **self.get_dummy_inputs(a_       ),       return_dict=a_,       )[0]

    UpperCamelCase__			    =    image[0, -10:]
    UpperCamelCase__			    =    image_from_tuple[0, -10:]

    assert image.shape == (1, 32)

    UpperCamelCase__			    =    np.array(
        [
            0.1_071_284,
            1.3_330_271,
            0.61_260_223,
            -0.6_691_065,
            -0.3_846_852,
            -1.0_303_661,
            0.22_716_111,
            0.03_348_901,
            0.30_040_675,
            -0.24_805_029,
        ]       )

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

 @skip_mps
 def 		lowercase_    (			self			:						Optional[int]       ):





    """simple docstring"""



    UpperCamelCase__			    =    torch_device == "cpu"
    UpperCamelCase__			    =    True
    UpperCamelCase__			    =    False

    self._test_inference_batch_single_identical(
        test_max_difference=a_,       relax_max_difference=a_,       test_mean_pixel_difference=a_,       )

 @skip_mps
 def 		lowercase_    (			self			:						Optional[int]       ):





    """simple docstring"""



    UpperCamelCase__			    =    torch_device == "cpu"
    UpperCamelCase__			    =    False

    self._test_attention_slicing_forward_pass(
        test_max_difference=a_,       test_mean_pixel_difference=a_,       )