




'''simple docstring'''


from decimal import Decimal, getcontext
from math import ceil, factorial
def 						snake_case_       (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''' )

							_a      	=							precision
							_a      	=							ceil(precision / 14 )
							_a      	=							42_6880 * Decimal(1_0005 ).sqrt()
							_a      	=							1
							_a      	=							1359_1409
							_a      	=							Decimal(UpperCamelCase )
							for k in range(1					,		UpperCamelCase ):
														_a      	=							factorial(6 * k ) // (factorial(3 * k ) * factorial(UpperCamelCase ) ** 3)
														linear_term += 5_4514_0134
														exponential_term *= -26_2537_4126_4076_8000
														partial_sum += Decimal(multinomial_term * linear_term ) / exponential_term
							return str(constant_term / partial_sum )[:-1]


if __name__ == "__main__":
				_snake_case : Optional[Any]  				=						50
				print(F'''The first {n} digits of pi is: {pi(n)}''')







'''simple docstring'''


from typing import Dict, List, Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import (
    center_crop,
    get_resize_output_image_size,
    normalize,
    rescale,
    resize,
    to_channel_dimension_format,
)
from ...image_utils import (
    IMAGENET_DEFAULT_MEAN,
    IMAGENET_DEFAULT_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    is_batched,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, logging


_snake_case : Dict  				=						logging.get_logger(__name__)

class      A       (						_a       ):
							lowercase_							     =							['pixel_values']







							def __init__(    self			:    List[Any]				,     lowerCAmelCase_			:    bool = True				,     lowerCAmelCase_			:    Optional[Dict[str, int]] = None				,     lowerCAmelCase_			:    PILImageResampling = PILImageResampling.BICUBIC				,     lowerCAmelCase_			:    bool = True				,     lowerCAmelCase_			:    bool = True				,     lowerCAmelCase_			:    Union[int, float] = 1 / 2_55				,     lowerCAmelCase_			:    Dict[str, int] = None				,     lowerCAmelCase_			:    bool = True				,     lowerCAmelCase_			:    Optional[Union[float, List[float]]] = None				,     lowerCAmelCase_			:    Optional[Union[float, List[float]]] = None				,     **lowerCAmelCase_			:    int				,     )     ->				None:


														"""simple docstring"""


														super().__init__(**lowerCAmelCase_   )
														_a      	=							size if size is not None else {'''height''': 2_24, '''width''': 2_24}
														_a      	=							get_size_dict(lowerCAmelCase_   )
														_a      	=							crop_size if crop_size is not None else {'''height''': 2_24, '''width''': 2_24}
														_a      	=							get_size_dict(lowerCAmelCase_				,     default_to_square=lowerCAmelCase_				,     param_name='''crop_size'''   )

														_a      	=							do_resize
														_a      	=							do_rescale
														_a      	=							do_normalize
														_a      	=							do_center_crop
														_a      	=							crop_size
														_a      	=							size
														_a      	=							resample
														_a      	=							rescale_factor
														_a      	=							image_mean if image_mean is not None else IMAGENET_DEFAULT_MEAN
														_a      	=							image_std if image_std is not None else IMAGENET_DEFAULT_STD







							def   __lowerCAmelCase     (    self			:    Optional[int]				,     lowerCAmelCase_			:    np.ndarray				,     lowerCAmelCase_			:    Dict[str, int]				,     lowerCAmelCase_			:    PILImageResampling = PILImageResampling.BILINEAR				,     lowerCAmelCase_			:    Optional[Union[str, ChannelDimension]] = None				,     **lowerCAmelCase_			:    int				,     )     ->				np.ndarray:


														"""simple docstring"""


														_a      	=							get_size_dict(lowerCAmelCase_   )

														if "shortest_edge" in size:
																					_a      	=							get_resize_output_image_size(lowerCAmelCase_				,     size=size['''shortest_edge''']				,     default_to_square=lowerCAmelCase_   )
																					# size = get_resize_output_image_size(image, size["shortest_edge"], size["longest_edge"])
														elif "height" in size and "width" in size:
																					_a      	=							(size['''height'''], size['''width'''])
														else:
																					raise ValueError(F'Size must contain \'height\' and \'width\' keys or \'shortest_edge\' key. Got {size.keys()}'   )
														return resize(lowerCAmelCase_				,     size=lowerCAmelCase_				,     resample=lowerCAmelCase_				,     data_format=lowerCAmelCase_				,     **lowerCAmelCase_   )







							def   __lowerCAmelCase     (    self			:    Optional[int]				,     lowerCAmelCase_			:    np.ndarray				,     lowerCAmelCase_			:    Dict[str, int]				,     lowerCAmelCase_			:    Optional[Union[str, ChannelDimension]] = None				,     **lowerCAmelCase_			:    Dict				,     )     ->				np.ndarray:


														"""simple docstring"""


														_a      	=							get_size_dict(lowerCAmelCase_   )
														if "height" not in size or "width" not in size:
																					raise ValueError(F'The `size` parameter must contain the keys (height, width). Got {size.keys()}'   )
														return center_crop(lowerCAmelCase_				,     size=(size['''height'''], size['''width'''])				,     data_format=lowerCAmelCase_				,     **lowerCAmelCase_   )







							def   __lowerCAmelCase     (    self			:    Tuple				,     lowerCAmelCase_			:    np.ndarray				,     lowerCAmelCase_			:    float				,     lowerCAmelCase_			:    Optional[Union[str, ChannelDimension]] = None				,     **lowerCAmelCase_			:    List[Any]   )     ->				np.ndarray:


														"""simple docstring"""


														return rescale(lowerCAmelCase_				,     scale=lowerCAmelCase_				,     data_format=lowerCAmelCase_				,     **lowerCAmelCase_   )







							def   __lowerCAmelCase     (    self			:    int				,     lowerCAmelCase_			:    np.ndarray				,     lowerCAmelCase_			:    Union[float, List[float]]				,     lowerCAmelCase_			:    Union[float, List[float]]				,     lowerCAmelCase_			:    Optional[Union[str, ChannelDimension]] = None				,     **lowerCAmelCase_			:    List[Any]				,     )     ->				np.ndarray:


														"""simple docstring"""


														return normalize(lowerCAmelCase_				,     mean=lowerCAmelCase_				,     std=lowerCAmelCase_				,     data_format=lowerCAmelCase_				,     **lowerCAmelCase_   )







							def   __lowerCAmelCase     (    self			:    int				,     lowerCAmelCase_			:    ImageInput				,     lowerCAmelCase_			:    Optional[bool] = None				,     lowerCAmelCase_			:    Dict[str, int] = None				,     lowerCAmelCase_			:    PILImageResampling = None				,     lowerCAmelCase_			:    bool = None				,     lowerCAmelCase_			:    int = None				,     lowerCAmelCase_			:    Optional[bool] = None				,     lowerCAmelCase_			:    Optional[float] = None				,     lowerCAmelCase_			:    Optional[bool] = None				,     lowerCAmelCase_			:    Optional[Union[float, List[float]]] = None				,     lowerCAmelCase_			:    Optional[Union[float, List[float]]] = None				,     lowerCAmelCase_			:    Optional[Union[str, TensorType]] = None				,     lowerCAmelCase_			:    Union[str, ChannelDimension] = ChannelDimension.FIRST				,     **lowerCAmelCase_			:    List[str]				,     )     ->				BatchFeature:


														"""simple docstring"""


														_a      	=							do_resize if do_resize is not None else self.do_resize
														_a      	=							do_rescale if do_rescale is not None else self.do_rescale
														_a      	=							do_normalize if do_normalize is not None else self.do_normalize
														_a      	=							do_center_crop if do_center_crop is not None else self.do_center_crop
														_a      	=							crop_size if crop_size is not None else self.crop_size
														_a      	=							get_size_dict(lowerCAmelCase_				,     param_name='''crop_size'''				,     default_to_square=lowerCAmelCase_   )
														_a      	=							resample if resample is not None else self.resample
														_a      	=							rescale_factor if rescale_factor is not None else self.rescale_factor
														_a      	=							image_mean if image_mean is not None else self.image_mean
														_a      	=							image_std if image_std is not None else self.image_std

														_a      	=							size if size is not None else self.size
														_a      	=							get_size_dict(lowerCAmelCase_   )

														if not is_batched(lowerCAmelCase_   ):
																					_a      	=							[images]

														if not valid_images(lowerCAmelCase_   ):
																					raise ValueError(
																					    '''Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, '''
																					    '''torch.Tensor, tf.Tensor or jax.ndarray.'''   )

														if do_resize and size is None:
																					raise ValueError('''Size must be specified if do_resize is True.'''   )

														if do_center_crop and crop_size is None:
																					raise ValueError('''Crop size must be specified if do_center_crop is True.'''   )

														if do_rescale and rescale_factor is None:
																					raise ValueError('''Rescale factor must be specified if do_rescale is True.'''   )

														# All transformations expect numpy arrays.
														_a      	=							[to_numpy_array(lowerCAmelCase_   ) for image in images]

														if do_resize:
																					_a      	=							[self.resize(image=lowerCAmelCase_				,     size=lowerCAmelCase_				,     resample=lowerCAmelCase_   ) for image in images]

														if do_center_crop:
																					_a      	=							[self.center_crop(image=lowerCAmelCase_				,     size=lowerCAmelCase_   ) for image in images]

														if do_rescale:
																					_a      	=							[self.rescale(image=lowerCAmelCase_				,     scale=lowerCAmelCase_   ) for image in images]

														if do_normalize:
																					_a      	=							[self.normalize(image=lowerCAmelCase_				,     mean=lowerCAmelCase_				,     std=lowerCAmelCase_   ) for image in images]

														_a      	=							[to_channel_dimension_format(lowerCAmelCase_				,     lowerCAmelCase_   ) for image in images]

														_a      	=							{'''pixel_values''': images}
														return BatchFeature(data=lowerCAmelCase_				,     tensor_type=lowerCAmelCase_   )

