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


__a  :     Dict       =  logging.get_logger(__name__)




class    _UpperCamelCase      (						_UpperCAmelCase ):


			"""simple docstring"""






			__a  : List[Any]			 =						['''pixel_values''']





			def __init__(   self      ,   lowerCAmelCase__ = True      ,   lowerCAmelCase__ = None      ,   lowerCAmelCase__ = PILImageResampling.BICUBIC      ,   lowerCAmelCase__ = True      ,   lowerCAmelCase__ = True      ,   lowerCAmelCase__ = 1 / 2_55      ,   lowerCAmelCase__ = None      ,   lowerCAmelCase__ = True      ,   lowerCAmelCase__ = None      ,   lowerCAmelCase__ = None      ,   **lowerCAmelCase__      ,   )     ->					None:

							'''simple docstring'''


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

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





			def        _SCREAMING_SNAKE_CASE			(   self      ,   lowerCAmelCase__      ,   lowerCAmelCase__      ,   lowerCAmelCase__ = PILImageResampling.BILINEAR      ,   lowerCAmelCase__ = None      ,   **lowerCAmelCase__      ,   )     ->					np.ndarray:

							'''simple docstring'''


							__lowercase 			=							get_size_dict(lowerCAmelCase__						)

							if "shortest_edge" in size:
											__lowercase 			=							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:
											__lowercase 			=							(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        _SCREAMING_SNAKE_CASE			(   self      ,   lowerCAmelCase__      ,   lowerCAmelCase__      ,   lowerCAmelCase__ = None      ,   **lowerCAmelCase__      ,   )     ->					np.ndarray:

							'''simple docstring'''


							__lowercase 			=							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        _SCREAMING_SNAKE_CASE			(   self      ,   lowerCAmelCase__      ,   lowerCAmelCase__      ,   lowerCAmelCase__ = None      ,   **lowerCAmelCase__						)     ->					np.ndarray:

							'''simple docstring'''


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





			def        _SCREAMING_SNAKE_CASE			(   self      ,   lowerCAmelCase__      ,   lowerCAmelCase__      ,   lowerCAmelCase__      ,   lowerCAmelCase__ = None      ,   **lowerCAmelCase__      ,   )     ->					np.ndarray:

							'''simple docstring'''


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





			def        _SCREAMING_SNAKE_CASE			(   self      ,   lowerCAmelCase__      ,   lowerCAmelCase__ = None      ,   lowerCAmelCase__ = None      ,   lowerCAmelCase__ = None      ,   lowerCAmelCase__ = None      ,   lowerCAmelCase__ = None      ,   lowerCAmelCase__ = None      ,   lowerCAmelCase__ = None      ,   lowerCAmelCase__ = None      ,   lowerCAmelCase__ = None      ,   lowerCAmelCase__ = None      ,   lowerCAmelCase__ = None      ,   lowerCAmelCase__ = ChannelDimension.FIRST      ,   **lowerCAmelCase__      ,   )     ->					BatchFeature:

							'''simple docstring'''


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

							__lowercase 			=							size if size is not None else self.size
							__lowercase 			=							get_size_dict(lowerCAmelCase__						)

							if not is_batched(lowerCAmelCase__						):
											__lowercase 			=							[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.
							__lowercase 			=							[to_numpy_array(lowerCAmelCase__						) for image in images]

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

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

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

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

							__lowercase 			=							[to_channel_dimension_format(lowerCAmelCase__      ,   lowerCAmelCase__						) for image in images]

							__lowercase 			=							{'''pixel_values''': images}
							return BatchFeature(data=lowerCAmelCase__      ,   tensor_type=lowerCAmelCase__						)
from decimal import Decimal, getcontext
from math import ceil, factorial





def 				UpperCAmelCase						(    lowercase							):







				"""simple docstring"""



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

				__lowercase 			=							precision
				__lowercase 			=							ceil(precision / 14							)
				__lowercase 			=							426880 * Decimal(10005							).sqrt()
				__lowercase 			=							1
				__lowercase 			=							13591409
				__lowercase 			=							Decimal(lowercase							)
				for k in range(1							,			lowercase							):
								__lowercase 			=							factorial(6 * k							) // (factorial(3 * k							) * factorial(lowercase							) ** 3)
								linear_term += 545140134
								exponential_term *= -262537412640768000
								partial_sum += Decimal(multinomial_term * linear_term							) / exponential_term
				return str(constant_term / partial_sum							)[:-1]


if __name__ == "__main__":
		__a  :     Optional[Any]       =  5_0
		print(F'''The first {n} digits of pi is: {pi(n)}''')