


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,
    convert_to_rgb,
    get_resize_output_image_size,
    normalize,
    rescale,
    resize,
    to_channel_dimension_format,
)
from ...image_utils import (
    OPENAI_CLIP_MEAN,
    OPENAI_CLIP_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


__lowerCamelCase        =     logging.get_logger(__name__)


if is_vision_available():
       import PIL


class   a__	(						lowerCAmelCase_    ):
       lowerCamelCase__:     Optional[int]							    =     ["""pixel_values"""]

       def __init__(   self      :     Dict      ,							lowerCamelCase_      :     bool = True      ,							lowerCamelCase_      :     Dict[str, int] = None      ,							lowerCamelCase_      :     PILImageResampling = PILImageResampling.BICUBIC      ,							lowerCamelCase_      :     bool = True      ,							lowerCamelCase_      :     Dict[str, int] = None      ,							lowerCamelCase_      :     bool = True      ,							lowerCamelCase_      :     Union[int, float] = 1 / 2_5_5      ,							lowerCamelCase_      :     bool = True      ,							lowerCamelCase_      :     Optional[Union[float, List[float]]] = None      ,							lowerCamelCase_      :     Optional[Union[float, List[float]]] = None      ,							lowerCamelCase_      :     bool = True      ,							**lowerCamelCase_      :     Union[str, Any]      ,							):
            super().__init__(**lowerCamelCase_    )
            a_    :     Tuple										=    size if size is not None else {"""shortest_edge""": 2_2_4}
            a_    :     Tuple										=    get_size_dict(lowerCamelCase_      ,							default_to_square=lowerCamelCase_    )
            a_    :     Tuple										=    crop_size if crop_size is not None else {"""height""": 2_2_4, """width""": 2_2_4}
            a_    :     List[str]										=    get_size_dict(lowerCamelCase_      ,							default_to_square=lowerCamelCase_      ,							param_name="""crop_size"""    )

            a_    :     int										=    do_resize
            a_    :     Tuple										=    size
            a_    :     Any										=    resample
            a_    :     Union[str, Any]										=    do_center_crop
            a_    :     str										=    crop_size
            a_    :     Dict										=    do_rescale
            a_    :     int										=    rescale_factor
            a_    :     Tuple										=    do_normalize
            a_    :     Union[str, Any]										=    image_mean if image_mean is not None else OPENAI_CLIP_MEAN
            a_    :     List[Any]										=    image_std if image_std is not None else OPENAI_CLIP_STD
            a_    :     List[Any]										=    do_convert_rgb

       def 						UpperCAmelCase(   self      :     str      ,							lowerCamelCase_      :     np.ndarray      ,							lowerCamelCase_      :     Dict[str, int]      ,							lowerCamelCase_      :     PILImageResampling = PILImageResampling.BICUBIC      ,							lowerCamelCase_      :     Optional[Union[str, ChannelDimension]] = None      ,							**lowerCamelCase_      :     Tuple      ,							):
            a_    :     Tuple										=    get_size_dict(lowerCamelCase_      ,							default_to_square=lowerCamelCase_    )
            if "shortest_edge" not in size:
                 raise ValueError(F'''The `size` parameter must contain the key `shortest_edge`. Got {size.keys()}'''    )
            a_    :     str										=    get_resize_output_image_size(lowerCamelCase_      ,							size=size["""shortest_edge"""]      ,							default_to_square=lowerCamelCase_    )
            return resize(lowerCamelCase_      ,							size=lowerCamelCase_      ,							resample=lowerCamelCase_      ,							data_format=lowerCamelCase_      ,							**lowerCamelCase_    )

       def 						UpperCAmelCase(   self      :     Dict      ,							lowerCamelCase_      :     np.ndarray      ,							lowerCamelCase_      :     Dict[str, int]      ,							lowerCamelCase_      :     Optional[Union[str, ChannelDimension]] = None      ,							**lowerCamelCase_      :     Dict      ,							):
            a_    :     List[Any]										=    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 						UpperCAmelCase(   self      :     List[Any]      ,							lowerCamelCase_      :     np.ndarray      ,							lowerCamelCase_      :     Union[int, float]      ,							lowerCamelCase_      :     Optional[Union[str, ChannelDimension]] = None      ,							**lowerCamelCase_      :     List[str]      ,							):
            return rescale(lowerCamelCase_      ,							scale=lowerCamelCase_      ,							data_format=lowerCamelCase_      ,							**lowerCamelCase_    )

       def 						UpperCAmelCase(   self      :     Union[str, Any]      ,							lowerCamelCase_      :     np.ndarray      ,							lowerCamelCase_      :     Union[float, List[float]]      ,							lowerCamelCase_      :     Union[float, List[float]]      ,							lowerCamelCase_      :     Optional[Union[str, ChannelDimension]] = None      ,							**lowerCamelCase_      :     Any      ,							):
            return normalize(lowerCamelCase_      ,							mean=lowerCamelCase_      ,							std=lowerCamelCase_      ,							data_format=lowerCamelCase_      ,							**lowerCamelCase_    )

       def 						UpperCAmelCase(   self      :     Optional[int]      ,							lowerCamelCase_      :     ImageInput      ,							lowerCamelCase_      :     bool = None      ,							lowerCamelCase_      :     Dict[str, int] = None      ,							lowerCamelCase_      :     PILImageResampling = None      ,							lowerCamelCase_      :     bool = None      ,							lowerCamelCase_      :     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_      :     bool = None      ,							lowerCamelCase_      :     Optional[Union[str, TensorType]] = None      ,							lowerCamelCase_      :     Optional[ChannelDimension] = ChannelDimension.FIRST      ,							**lowerCamelCase_      :     Any      ,							):
            a_    :     List[str]										=    do_resize if do_resize is not None else self.do_resize
            a_    :     Optional[Any]										=    size if size is not None else self.size
            a_    :     Dict										=    get_size_dict(lowerCamelCase_      ,							param_name="""size"""      ,							default_to_square=lowerCamelCase_    )
            a_    :     Optional[int]										=    resample if resample is not None else self.resample
            a_    :     Optional[int]										=    do_center_crop if do_center_crop is not None else self.do_center_crop
            a_    :     List[str]										=    crop_size if crop_size is not None else self.crop_size
            a_    :     List[Any]										=    get_size_dict(lowerCamelCase_      ,							param_name="""crop_size"""      ,							default_to_square=lowerCamelCase_    )
            a_    :     int										=    do_rescale if do_rescale is not None else self.do_rescale
            a_    :     Optional[Any]										=    rescale_factor if rescale_factor is not None else self.rescale_factor
            a_    :     str										=    do_normalize if do_normalize is not None else self.do_normalize
            a_    :     Tuple										=    image_mean if image_mean is not None else self.image_mean
            a_    :     List[str]										=    image_std if image_std is not None else self.image_std
            a_    :     str										=    do_convert_rgb if do_convert_rgb is not None else self.do_convert_rgb

            a_    :     Optional[int]										=    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:
                 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."""    )

            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."""    )

            # PIL RGBA images are converted to RGB
            if do_convert_rgb:
                 a_    :     Tuple										=    [convert_to_rgb(lowerCamelCase_    ) for image in images]

            # All transformations expect numpy arrays.
            a_    :     Tuple										=    [to_numpy_array(lowerCamelCase_    ) for image in images]

            if do_resize:
                 a_    :     List[str]										=    [self.resize(image=lowerCamelCase_      ,							size=lowerCamelCase_      ,							resample=lowerCamelCase_    ) for image in images]

            if do_center_crop:
                 a_    :     Dict										=    [self.center_crop(image=lowerCamelCase_      ,							size=lowerCamelCase_    ) for image in images]

            if do_rescale:
                 a_    :     Tuple										=    [self.rescale(image=lowerCamelCase_      ,							scale=lowerCamelCase_    ) for image in images]

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

            a_    :     List[Any]										=    [to_channel_dimension_format(lowerCamelCase_      ,							lowerCamelCase_    ) for image in images]

            a_    :     Tuple										=    {"""pixel_values""": images}
            return BatchFeature(data=lowerCamelCase_      ,							tensor_type=lowerCamelCase_    )







from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt



def  _a			(						__UpperCamelCase ):
     a_    :     int										=    int(number**0.5 )
     return number == sq * sq



def  _a			(						__UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase ):
     a_    :     int										=    x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
     a_    :     int										=    x_den * y_den * z_den
     a_    :     int										=    gcd(__UpperCamelCase  ,  __UpperCamelCase )
     top //= hcf
     bottom //= hcf
     return top, bottom



def  _a			(						__UpperCamelCase = 3_5 ):
     a_    :     set										=    set()
     a_    :     int
     a_    :     Fraction										=    Fraction(0 )
     a_    :     tuple[int, int]

     for x_num in range(1  ,  order + 1 ):
          for x_den in range(x_num + 1  ,  order + 1 ):
               for y_num in range(1  ,  order + 1 ):
                    for y_den in range(y_num + 1  ,  order + 1 ):
                         # n=1
                         a_    :     int										=    x_num * y_den + x_den * y_num
                         a_    :     Optional[int]										=    x_den * y_den
                         a_    :     Optional[Any]										=    gcd(__UpperCamelCase  ,  __UpperCamelCase )
                         z_num //= hcf
                         z_den //= hcf
                         if 0 < z_num < z_den <= order:
                              a_    :     Optional[int]										=    add_three(
                                  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase )
                              unique_s.add(__UpperCamelCase )

                         # n=2
                         a_    :     List[Any]										=    (
                             x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
                         )
                         a_    :     str										=    x_den * x_den * y_den * y_den
                         if is_sq(__UpperCamelCase ) and is_sq(__UpperCamelCase ):
                              a_    :     Optional[Any]										=    int(sqrt(__UpperCamelCase ) )
                              a_    :     Optional[int]										=    int(sqrt(__UpperCamelCase ) )
                              a_    :     Optional[Any]										=    gcd(__UpperCamelCase  ,  __UpperCamelCase )
                              z_num //= hcf
                              z_den //= hcf
                              if 0 < z_num < z_den <= order:
                                   a_    :     str										=    add_three(
                                       __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase )
                                   unique_s.add(__UpperCamelCase )

                    # n=-1
                         a_    :     Union[str, Any]										=    x_num * y_num
                         a_    :     Tuple										=    x_den * y_num + x_num * y_den
                         a_    :     List[Any]										=    gcd(__UpperCamelCase  ,  __UpperCamelCase )
                         z_num //= hcf
                         z_den //= hcf
                         if 0 < z_num < z_den <= order:
                              a_    :     Union[str, Any]										=    add_three(
                                  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase )
                              unique_s.add(__UpperCamelCase )

                         # n=2
                         a_    :     Union[str, Any]										=    x_num * x_num * y_num * y_num
                         a_    :     Dict										=    (
                             x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
                         )
                         if is_sq(__UpperCamelCase ) and is_sq(__UpperCamelCase ):
                              a_    :     Dict										=    int(sqrt(__UpperCamelCase ) )
                              a_    :     Union[str, Any]										=    int(sqrt(__UpperCamelCase ) )
                              a_    :     Dict										=    gcd(__UpperCamelCase  ,  __UpperCamelCase )
                              z_num //= hcf
                              z_den //= hcf
                              if 0 < z_num < z_den <= order:
                                   a_    :     List[Any]										=    add_three(
                                       __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase )
                                   unique_s.add(__UpperCamelCase )

     for num, den in unique_s:
          total += Fraction(__UpperCamelCase  ,  __UpperCamelCase )

     return total.denominator + total.numerator


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



