



"""simple docstring"""


def 					_lowerCAmelCase (  lowercase_		):
						UpperCAmelCase			 =					1
						UpperCAmelCase			 =					0
						UpperCAmelCase			 =					1
						UpperCAmelCase			 =					1
						UpperCAmelCase			 =					3
						UpperCAmelCase			 =					3
						UpperCAmelCase			 =					limit
						UpperCAmelCase			 =					0

						UpperCAmelCase			 =					''
						while counter != decimal + 1:
												if 4 * q + r - t < n * t:
																		result += str(lowercase_		)
																		if counter == 0:
																								result += "."

																		if decimal == counter:
																								break

																		counter += 1
																		UpperCAmelCase			 =					10 * (r - n * t)
																		UpperCAmelCase			 =					((10 * (3 * q + r)) // t) - 10 * n
																		q *= 10
																		UpperCAmelCase			 =					nr
												else:
																		UpperCAmelCase			 =					(2 * q + r) * l
																		UpperCAmelCase			 =					(q * (7 * k) + 2 + (r * l)) // (t * l)
																		q *= k
																		t *= l
																		l += 2
																		k += 1
																		UpperCAmelCase			 =					nn
																		UpperCAmelCase			 =					nr
						return result

def 					_lowerCAmelCase (  ):
						print(F"""{calculate_pi(50		) = }"""		)
						import doctest

						doctest.testmod()


if __name__ == "__main__":
				main()






'''simple docstring'''




from dataclasses import dataclass
from typing import List, Optional, Union

import numpy as np
import PIL
from PIL import Image

from ...utils import BaseOutput, is_torch_available, is_transformers_available


@dataclass
# Copied from diffusers.pipelines.stable_diffusion.__init__.StableDiffusionPipelineOutput with Stable->Alt
class    UpperCAmelCase__	(							_snake_case      ):






   """simple docstring"""
   A				:							Union[List[PIL.Image.Image], np.ndarray]
   A				:							Optional[List[bool]]


if is_transformers_available() and is_torch_available():
 from .modeling_roberta_series import RobertaSeriesModelWithTransformation
 from .pipeline_alt_diffusion import AltDiffusionPipeline
 from .pipeline_alt_diffusion_imgaimg import AltDiffusionImgaImgPipeline




