






'''simple docstring'''
import os

from huggingface_hub.constants import HUGGINGFACE_HUB_CACHE, hf_cache_home


a_					=	HUGGINGFACE_HUB_CACHE


a_					=	'config.json'
a_					=	'diffusion_pytorch_model.bin'
a_					=	'diffusion_flax_model.msgpack'
a_					=	'model.onnx'
a_					=	'diffusion_pytorch_model.safetensors'
a_					=	'weights.pb'
a_					=	'https://huggingface.co'
a_					=	default_cache_path
a_					=	'diffusers_modules'
a_					=	os.getenv('HF_MODULES_CACHE', os.path.join(hf_cache_home, 'modules'))
a_					=	['fp16', 'non-ema']
a_					=	'.self_attn'








'''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)}''')