"""simple docstring"""
import math







def 						__a       (     _SCREAMING_SNAKE_CASE       )     ->bool:

  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(_SCREAMING_SNAKE_CASE       ) + 1       )		,					6       ):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True







def 						__a       (     _SCREAMING_SNAKE_CASE = 10001       )     ->int:

  try:
    a__:					Dict      							=     int(_SCREAMING_SNAKE_CASE       )
  except (TypeError, ValueError):
    raise TypeError('Parameter nth must be int or castable to int.'       ) from None
  if nth <= 0:
    raise ValueError('Parameter nth must be greater than or equal to one.'       )
  a__:					list[int]      							=     []
  a__:					Tuple      							=     2
  while len(_SCREAMING_SNAKE_CASE       ) < nth:
    if is_prime(_SCREAMING_SNAKE_CASE       ):
      primes.append(_SCREAMING_SNAKE_CASE       )
      num += 1
    else:
      num += 1
  return primes[len(_SCREAMING_SNAKE_CASE       ) - 1]


if __name__ == "__main__":
 print(f"{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        __snake_case	(					unittest.TestCase    ):



      @property
      def   lowerCamelCase_       (						self)     ->      Dict:





        '''simple docstring'''





        torch.manual_seed(0)
        a__:					str      							=     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   lowerCamelCase_       (						self)     ->      int:





        '''simple docstring'''





        torch.manual_seed(0)
        a__:					List[Any]      							=     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   lowerCamelCase_       (						self)     ->      Optional[Any]:





        '''simple docstring'''





        torch.manual_seed(0)
        a__:					Optional[int]      							=     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   ,      )
        return CLIPTextModel(lowercase)



      def   lowerCamelCase_       (						self)     ->      str:





        '''simple docstring'''





        a__:					Union[str, Any]      							=     self.dummy_uncond_unet
        a__:					Optional[int]      							=     DDIMScheduler()
        a__:					Optional[int]      							=     self.dummy_vq_model

        a__:					Union[str, Any]      							=     LDMPipeline(unet=lowercase   ,      vqvae=lowercase   ,      scheduler=lowercase)
        ldm.to(lowercase)
        ldm.set_progress_bar_config(disable=lowercase)

        a__:					str      							=     torch.manual_seed(0)
        a__:					Dict      							=     ldm(generator=lowercase   ,      num_inference_steps=2   ,      output_type='numpy').images

        a__:					Union[str, Any]      							=     torch.manual_seed(0)
        a__:					int      							=     ldm(generator=lowercase   ,      num_inference_steps=2   ,      output_type='numpy'   ,      return_dict=lowercase)[0]

        a__:					Union[str, Any]      							=     image[0, -3:, -3:, -1]
        a__:					int      							=     image_from_tuple[0, -3:, -3:, -1]

        assert image.shape == (1, 64, 64, 3)
        a__:					int      							=     np.array([0.8512, 0.818, 0.6411, 0.6808, 0.4465, 0.5618, 0.46, 0.6231, 0.5172])
        a__:					Optional[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        __snake_case	(					unittest.TestCase    ):



      def   lowerCamelCase_       (						self)     ->      Optional[Any]:





        '''simple docstring'''





        a__:					Union[str, Any]      							=     LDMPipeline.from_pretrained('CompVis/ldm-celebahq-256')
        ldm.to(lowercase)
        ldm.set_progress_bar_config(disable=lowercase)

        a__:					List[str]      							=     torch.manual_seed(0)
        a__:					Optional[int]      							=     ldm(generator=lowercase   ,      num_inference_steps=5   ,      output_type='numpy').images

        a__:					Optional[int]      							=     image[0, -3:, -3:, -1]

        assert image.shape == (1, 2_56, 2_56, 3)
        a__:					int      							=     np.array([0.4399, 0.44975, 0.46825, 0.474, 0.4359, 0.4581, 0.45095, 0.4341, 0.4447])
        a__:					Any      							=     1e-2 if torch_device != 'mps' else 3e-2

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


