


def       _lowerCAmelCase    (				lowerCAmelCase_				:int = 10**12				)->int:
   '''simple docstring'''






   snake_case_            =       1
   snake_case_            =       0

   snake_case_            =       1
   snake_case_            =       1

   while numerator <= 2 * min_total - 1:
      prev_numerator += 2 * numerator
      numerator += 2 * prev_numerator

      prev_denominator += 2 * denominator
      denominator += 2 * prev_denominator

   return (denominator + 1) // 2


if __name__ == "__main__":
   print(F'''{solution() = }''')








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, normalize, rescale, resize, to_channel_dimension_format
from ...image_utils import (
    IMAGENET_STANDARD_MEAN,
    IMAGENET_STANDARD_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


if is_vision_available():
   import PIL


SCREAMING_SNAKE_CASE						:List[Any]			=  logging.get_logger(__name__)


class      __lowerCAmelCase  (			a       ):






  """simple docstring"""





  _SCREAMING_SNAKE_CASE		     =							['pixel_values']



  def __init__(  self							:							Optional[int]     ,					_lowerCAmelCase							:							bool = True     ,					_lowerCAmelCase							:							Dict[str, int] = None     ,					_lowerCAmelCase							:							PILImageResampling = PIL.Image.BICUBIC     ,					_lowerCAmelCase							:							bool = True     ,					_lowerCAmelCase							:							Dict[str, int] = None     ,					_lowerCAmelCase							:							Union[int, float] = 1 / 2_5_5     ,					_lowerCAmelCase							:							bool = True     ,					_lowerCAmelCase							:							bool = True     ,					_lowerCAmelCase							:							Optional[Union[float, List[float]]] = None     ,					_lowerCAmelCase							:							Optional[Union[float, List[float]]] = None     ,					**_lowerCAmelCase							:							Optional[Any]     ,					) ->			None:




     """simple docstring"""
     super().__init__(**_lowerCAmelCase	)
     snake_case_            =       size if size is not None else {"height": 2_5_6, "width": 2_5_6}
     snake_case_            =       get_size_dict(_lowerCAmelCase	)
     snake_case_            =       crop_size if crop_size is not None else {"height": 2_2_4, "width": 2_2_4}
     snake_case_            =       get_size_dict(_lowerCAmelCase     ,					param_name="crop_size"	)

     snake_case_            =       do_resize
     snake_case_            =       size
     snake_case_            =       resample
     snake_case_            =       do_center_crop
     snake_case_            =       crop_size
     snake_case_            =       do_rescale
     snake_case_            =       rescale_factor
     snake_case_            =       do_normalize
     snake_case_            =       image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
     snake_case_            =       image_std if image_std is not None else IMAGENET_STANDARD_STD



  def        lowerCAmelCase__	(  self							:							List[str]     ,					_lowerCAmelCase							:							np.ndarray     ,					_lowerCAmelCase							:							Dict[str, int]     ,					_lowerCAmelCase							:							PILImageResampling = PIL.Image.BICUBIC     ,					_lowerCAmelCase							:							Optional[Union[str, ChannelDimension]] = None     ,					**_lowerCAmelCase							:							int     ,					) ->			np.ndarray:




     """simple docstring"""
     snake_case_            =       get_size_dict(_lowerCAmelCase	)
     if "height" not in size or "width" not in size:
        raise ValueError(F'''The size dictionary must have keys \'height\' and \'width\'. Got {size.keys()}'''	)
     return resize(
         _lowerCAmelCase     ,					size=(size["height"], size["width"])     ,					resample=_lowerCAmelCase     ,					data_format=_lowerCAmelCase     ,					**_lowerCAmelCase	)



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




     """simple docstring"""
     snake_case_            =       get_size_dict(_lowerCAmelCase	)
     if "height" not in size or "width" not in size:
        raise ValueError(F'''The size dictionary must have keys \'height\' and \'width\'. Got {size.keys()}'''	)
     return center_crop(_lowerCAmelCase     ,					size=(size["height"], size["width"])     ,					data_format=_lowerCAmelCase     ,					**_lowerCAmelCase	)



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




     """simple docstring"""
     return rescale(_lowerCAmelCase     ,					scale=_lowerCAmelCase     ,					data_format=_lowerCAmelCase     ,					**_lowerCAmelCase	)



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




     """simple docstring"""
     return normalize(_lowerCAmelCase     ,					mean=_lowerCAmelCase     ,					std=_lowerCAmelCase     ,					data_format=_lowerCAmelCase     ,					**_lowerCAmelCase	)



  def        lowerCAmelCase__	(  self							:							Optional[Any]     ,					_lowerCAmelCase							:							ImageInput     ,					_lowerCAmelCase							:							bool = None     ,					_lowerCAmelCase							:							Dict[str, int] = None     ,					_lowerCAmelCase							:							int=None     ,					_lowerCAmelCase							:							bool = None     ,					_lowerCAmelCase							:							Dict[str, int] = None     ,					_lowerCAmelCase							:							bool = None     ,					_lowerCAmelCase							:							float = None     ,					_lowerCAmelCase							:							bool = None     ,					_lowerCAmelCase							:							Optional[Union[float, List[float]]] = None     ,					_lowerCAmelCase							:							Optional[Union[float, List[float]]] = None     ,					_lowerCAmelCase							:							Optional[Union[str, TensorType]] = None     ,					_lowerCAmelCase							:							ChannelDimension = ChannelDimension.FIRST     ,					**_lowerCAmelCase							:							Tuple     ,					) ->			PIL.Image.Image:




     """simple docstring"""
     snake_case_            =       do_resize if do_resize is not None else self.do_resize
     snake_case_            =       resample if resample is not None else self.resample
     snake_case_            =       do_center_crop if do_center_crop is not None else self.do_center_crop
     snake_case_            =       do_rescale if do_rescale is not None else self.do_rescale
     snake_case_            =       rescale_factor if rescale_factor is not None else self.rescale_factor
     snake_case_            =       do_normalize if do_normalize is not None else self.do_normalize
     snake_case_            =       image_mean if image_mean is not None else self.image_mean
     snake_case_            =       image_std if image_std is not None else self.image_std

     snake_case_            =       size if size is not None else self.size
     snake_case_            =       get_size_dict(_lowerCAmelCase	)
     snake_case_            =       crop_size if crop_size is not None else self.crop_size
     snake_case_            =       get_size_dict(_lowerCAmelCase     ,					param_name="crop_size"	)

     snake_case_            =       make_list_of_images(_lowerCAmelCase	)

     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 or resample is None:
        raise ValueError("Size and resample 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."	)

     if do_normalize and (image_mean is None or image_std is None):
        raise ValueError("Image mean and std must be specified if do_normalize is True."	)

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

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

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

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

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

     snake_case_            =       [to_channel_dimension_format(_lowerCAmelCase     ,					_lowerCAmelCase	) for image in images]

     snake_case_            =       {"pixel_values": images}
     return BatchFeature(data=_lowerCAmelCase     ,					tensor_type=_lowerCAmelCase	)




