






'''simple docstring'''
from decimal import Decimal, getcontext
from math import ceil, factorial





def 	_a(					UpperCamelCase__			:  int							):




      '''simple docstring'''






      if not isinstance(UpperCamelCase__,		UpperCamelCase__							):
            raise TypeError('''Undefined for non-integers'''							)
      elif precision < 1:
            raise ValueError('''Undefined for non-natural numbers'''							)

      SCREAMING_SNAKE_CASE__       :			Optional[Any]													=precision
      SCREAMING_SNAKE_CASE__       :			int													=ceil(precision / 1_4							)
      SCREAMING_SNAKE_CASE__       :			int													=4_2_6_8_8_0 * Decimal(1_0_0_0_5							).sqrt()
      SCREAMING_SNAKE_CASE__       :			Tuple													=1
      SCREAMING_SNAKE_CASE__       :			Any													=1_3_5_9_1_4_0_9
      SCREAMING_SNAKE_CASE__       :			List[Any]													=Decimal(UpperCamelCase__							)
      for k in range(1,		UpperCamelCase__							):
            SCREAMING_SNAKE_CASE__       :			str													=factorial(6 * k							) // (factorial(3 * k							) * factorial(UpperCamelCase__							) ** 3)
            linear_term += 5_4_5_1_4_0_1_3_4
            exponential_term *= -2_6_2_5_3_7_4_1_2_6_4_0_7_6_8_0_0_0
            partial_sum += Decimal(multinomial_term * linear_term							) / exponential_term
      return str(constant_term / partial_sum							)[:-1]


if __name__ == "__main__":
  a_					=	5_0
  print(F'''The first {n} digits of pi is: {pi(n)}''')







'''simple docstring'''
import gc
import unittest

import numpy as np
import torch

from diffusers import StableDiffusionKDiffusionPipeline
from diffusers.utils import slow, torch_device
from diffusers.utils.testing_utils import enable_full_determinism, require_torch_gpu


enable_full_determinism()






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




 def        __magic_name__		( self		:							List[str] )		->  Optional[Any]:
       # clean up the VRAM after each test
       super().tearDown()
       gc.collect()
       torch.cuda.empty_cache()




 def        __magic_name__		( self		:							Union[str, Any] )		->  Dict:
       SCREAMING_SNAKE_CASE__       :			Optional[int]													=StableDiffusionKDiffusionPipeline.from_pretrained('''CompVis/stable-diffusion-v1-4''' )
       SCREAMING_SNAKE_CASE__       :			str													=sd_pipe.to(__lowercase )
       sd_pipe.set_progress_bar_config(disable=__lowercase )

       sd_pipe.set_scheduler('''sample_euler''' )

       SCREAMING_SNAKE_CASE__       :			List[Any]													='''A painting of a squirrel eating a burger'''
       SCREAMING_SNAKE_CASE__       :			List[str]													=torch.manual_seed(0 )
       SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=sd_pipe([prompt]   , generator=__lowercase   , guidance_scale=9.0   , num_inference_steps=20   , output_type='''np''' )

       SCREAMING_SNAKE_CASE__       :			Optional[Any]													=output.images

       SCREAMING_SNAKE_CASE__       :			int													=image[0, -3:, -3:, -1]

       assert image.shape == (1, 5_12, 5_12, 3)
       SCREAMING_SNAKE_CASE__       :			Any													=np.array([0.0447, 0.0492, 0.0468, 0.0408, 0.0383, 0.0408, 0.0354, 0.0380, 0.0339] )

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




 def        __magic_name__		( self		:							List[str] )		->  List[Any]:
       SCREAMING_SNAKE_CASE__       :			List[str]													=StableDiffusionKDiffusionPipeline.from_pretrained('''stabilityai/stable-diffusion-2-1-base''' )
       SCREAMING_SNAKE_CASE__       :			int													=sd_pipe.to(__lowercase )
       sd_pipe.set_progress_bar_config(disable=__lowercase )

       sd_pipe.set_scheduler('''sample_euler''' )

       SCREAMING_SNAKE_CASE__       :			Any													='''A painting of a squirrel eating a burger'''
       SCREAMING_SNAKE_CASE__       :			Dict													=torch.manual_seed(0 )
       SCREAMING_SNAKE_CASE__       :			Tuple													=sd_pipe([prompt]   , generator=__lowercase   , guidance_scale=9.0   , num_inference_steps=20   , output_type='''np''' )

       SCREAMING_SNAKE_CASE__       :			Dict													=output.images

       SCREAMING_SNAKE_CASE__       :			Dict													=image[0, -3:, -3:, -1]

       assert image.shape == (1, 5_12, 5_12, 3)
       SCREAMING_SNAKE_CASE__       :			List[str]													=np.array([0.1237, 0.1320, 0.1438, 0.1359, 0.1390, 0.1132, 0.1277, 0.1175, 0.1112] )

       assert np.abs(image_slice.flatten() - expected_slice ).max() < 5e-1




 def        __magic_name__		( self		:							List[str] )		->  List[Any]:
       SCREAMING_SNAKE_CASE__       :			Any													=StableDiffusionKDiffusionPipeline.from_pretrained('''stabilityai/stable-diffusion-2-1-base''' )
       SCREAMING_SNAKE_CASE__       :			Tuple													=sd_pipe.to(__lowercase )
       sd_pipe.set_progress_bar_config(disable=__lowercase )

       sd_pipe.set_scheduler('''sample_dpmpp_2m''' )

       SCREAMING_SNAKE_CASE__       :			Tuple													='''A painting of a squirrel eating a burger'''
       SCREAMING_SNAKE_CASE__       :			Optional[Any]													=torch.manual_seed(0 )
       SCREAMING_SNAKE_CASE__       :			List[Any]													=sd_pipe(
           [prompt]   , generator=__lowercase   , guidance_scale=7.5   , num_inference_steps=15   , output_type='''np'''   , use_karras_sigmas=__lowercase   , )

       SCREAMING_SNAKE_CASE__       :			Optional[int]													=output.images

       SCREAMING_SNAKE_CASE__       :			Dict													=image[0, -3:, -3:, -1]

       assert image.shape == (1, 5_12, 5_12, 3)
       SCREAMING_SNAKE_CASE__       :			Optional[Any]													=np.array(
           [0.11381689, 0.12112921, 0.1389457, 0.12549606, 0.1244964, 0.10831517, 0.11562866, 0.10867816, 0.10499048] )

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