'''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, 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


__a: str          =   logging.get_logger(__name__)



class 			UpperCAmelCase  (						a__					):





       '''simple docstring'''



       SCREAMING_SNAKE_CASE							=    ["pixel_values"]

       def __init__(						self	,   __lowerCAmelCase = True	,   __lowerCAmelCase = None	,   __lowerCAmelCase = PIL.Image.BICUBIC	,   __lowerCAmelCase = True	,   __lowerCAmelCase = None	,   __lowerCAmelCase = 1 / 255	,   __lowerCAmelCase = True	,   __lowerCAmelCase = True	,   __lowerCAmelCase = None	,   __lowerCAmelCase = None	,   **__lowerCAmelCase	,   )  ->  None:
        super().__init__(**__lowerCAmelCase )
        lowercase__				:    Optional[Any]  =					size if size is not None else {'''height''': 256, '''width''': 256}
        lowercase__				:    List[str]  =					get_size_dict(__lowerCAmelCase )
        lowercase__				:    List[Any]  =					crop_size if crop_size is not None else {'''height''': 224, '''width''': 224}
        lowercase__				:    Union[str, Any]  =					get_size_dict(__lowerCAmelCase	,   param_name='''crop_size''' )

        lowercase__				:    Union[str, Any]  =					do_resize
        lowercase__				:    Dict  =					size
        lowercase__				:    Any  =					resample
        lowercase__				:    List[str]  =					do_center_crop
        lowercase__				:    Optional[int]  =					crop_size
        lowercase__				:    Optional[Any]  =					do_rescale
        lowercase__				:    List[Any]  =					rescale_factor
        lowercase__				:    Optional[int]  =					do_normalize
        lowercase__				:    Optional[int]  =					image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
        lowercase__				:    Dict  =					image_std if image_std is not None else IMAGENET_STANDARD_STD

       def _lowerCAmelCase(						self	,   __lowerCAmelCase	,   __lowerCAmelCase	,   __lowerCAmelCase = PIL.Image.BICUBIC	,   __lowerCAmelCase = None	,   **__lowerCAmelCase	,   )  ->  np.ndarray:
        lowercase__				:    Optional[Any]  =					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	,   __lowerCAmelCase	,   __lowerCAmelCase	,   __lowerCAmelCase = None	,   **__lowerCAmelCase	,   )  ->  np.ndarray:
        lowercase__				:    Tuple  =					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	,   __lowerCAmelCase	,   __lowerCAmelCase	,   __lowerCAmelCase = None	,   **__lowerCAmelCase	,   )  ->  Tuple:
        return rescale(__lowerCAmelCase	,   scale=__lowerCAmelCase	,   data_format=__lowerCAmelCase	,   **__lowerCAmelCase )

       def _lowerCAmelCase(						self	,   __lowerCAmelCase	,   __lowerCAmelCase	,   __lowerCAmelCase	,   __lowerCAmelCase = None	,   **__lowerCAmelCase	,   )  ->  np.ndarray:
        return normalize(__lowerCAmelCase	,   mean=__lowerCAmelCase	,   std=__lowerCAmelCase	,   data_format=__lowerCAmelCase	,   **__lowerCAmelCase )


       def _lowerCAmelCase(						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	,   )  ->  PIL.Image.Image:
        lowercase__				:    Optional[int]  =					do_resize if do_resize is not None else self.do_resize
        lowercase__				:    List[Any]  =					resample if resample is not None else self.resample
        lowercase__				:    List[str]  =					do_center_crop if do_center_crop is not None else self.do_center_crop
        lowercase__				:    List[str]  =					do_rescale if do_rescale is not None else self.do_rescale
        lowercase__				:    List[Any]  =					rescale_factor if rescale_factor is not None else self.rescale_factor
        lowercase__				:    Optional[int]  =					do_normalize if do_normalize is not None else self.do_normalize
        lowercase__				:    Union[str, Any]  =					image_mean if image_mean is not None else self.image_mean
        lowercase__				:    List[Any]  =					image_std if image_std is not None else self.image_std

        lowercase__				:    Tuple  =					size if size is not None else self.size
        lowercase__				:    Dict  =					get_size_dict(__lowerCAmelCase )
        lowercase__				:    int  =					crop_size if crop_size is not None else self.crop_size
        lowercase__				:    List[Any]  =					get_size_dict(__lowerCAmelCase	,   param_name='''crop_size''' )

        lowercase__				:    Any  =					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.
        lowercase__				:    int  =					[to_numpy_array(__lowerCAmelCase ) for image in images]

        if do_resize:
         lowercase__				:    Tuple  =					[self.resize(image=__lowerCAmelCase	,   size=__lowerCAmelCase	,   resample=__lowerCAmelCase ) for image in images]

        if do_center_crop:
         lowercase__				:    Union[str, Any]  =					[self.center_crop(image=__lowerCAmelCase	,   size=__lowerCAmelCase ) for image in images]

        if do_rescale:
         lowercase__				:    Optional[int]  =					[self.rescale(image=__lowerCAmelCase	,   scale=__lowerCAmelCase ) for image in images]

        if do_normalize:
         lowercase__				:    Optional[Any]  =					[self.normalize(image=__lowerCAmelCase	,   mean=__lowerCAmelCase	,   std=__lowerCAmelCase ) for image in images]

        lowercase__				:    Optional[Any]  =					[to_channel_dimension_format(__lowerCAmelCase	,   __lowerCAmelCase ) for image in images]

        lowercase__				:    Union[str, Any]  =					{'''pixel_values''': images}
        return BatchFeature(data=__lowerCAmelCase	,   tensor_type=__lowerCAmelCase )


'''simple docstring'''

from math import pow
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     ):
 if current_sum == needed_sum:
  # If the sum of the powers is equal to needed_sum, then we have a solution.
  solutions_count += 1
  return current_sum, solutions_count

 lowercase__				:    Optional[Any]  =					int(pow(UpperCAmelCase		,     UpperCAmelCase     )     )
 if current_sum + i_to_n <= needed_sum:
  # If the sum of the powers is less than needed_sum, then continue adding powers.
  current_sum += i_to_n
  lowercase__ ,							lowercase__				:    Dict  =					backtrack(
      UpperCAmelCase		,     UpperCAmelCase		,     current_number + 1		,     UpperCAmelCase		,     UpperCAmelCase     )
  current_sum -= i_to_n
 if i_to_n < needed_sum:
  # If the power of i is less than needed_sum, then try with the next power.
  lowercase__ ,							lowercase__				:    str  =					backtrack(
      UpperCAmelCase		,     UpperCAmelCase		,     current_number + 1		,     UpperCAmelCase		,     UpperCAmelCase     )
 return current_sum, solutions_count
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase     ):
 if not (1 <= needed_sum <= 1000 and 2 <= power <= 10):
  raise ValueError(
      '''Invalid input\n'''
      '''needed_sum must be between 1 and 1000, power between 2 and 10.'''     )

 return backtrack(UpperCAmelCase		,     UpperCAmelCase		,     1		,     0		,     0     )[1]  # Return the solutions_count


if __name__ == "__main__":
  import doctest

  doctest.testmod()

