



"""simple docstring"""







from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt

def     UpperCamelCase_   (   lowerCAmelCase__				:    int						)						->       bool:

  """simple docstring"""




  lowerCAmelCase_       :    int								=			int(number**0.5						)
  return number == sq * sq

def     UpperCamelCase_   (   lowerCAmelCase__				:    int   ,       lowerCAmelCase__				:    int   ,       lowerCAmelCase__				:    int   ,       lowerCAmelCase__				:    int   ,       lowerCAmelCase__				:    int   ,       lowerCAmelCase__				:    int						)						->       tuple[int, int]:

  """simple docstring"""




  lowerCAmelCase_       :    int								=			x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
  lowerCAmelCase_       :    int								=			x_den * y_den * z_den
  lowerCAmelCase_       :    int								=			gcd(lowerCAmelCase__   ,       lowerCAmelCase__						)
  top //= hcf
  bottom //= hcf
  return top, bottom

def     UpperCamelCase_   (   lowerCAmelCase__				:    int = 35						)						->       int:

  """simple docstring"""




  lowerCAmelCase_       :    set								=			set()
  lowerCAmelCase_       :    int
  lowerCAmelCase_       :    Fraction								=			Fraction(0						)
  lowerCAmelCase_       :    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
          lowerCAmelCase_       :    str								=			x_num * y_den + x_den * y_num
          lowerCAmelCase_       :    int								=			x_den * y_den
          lowerCAmelCase_       :    int								=			gcd(lowerCAmelCase__   ,       lowerCAmelCase__						)
          z_num //= hcf
          z_den //= hcf
          if 0 < z_num < z_den <= order:
            lowerCAmelCase_       :    List[str]								=			add_three(
                lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__						)
            unique_s.add(lowerCAmelCase__						)

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

                    # n=-1
          lowerCAmelCase_       :    Dict								=			x_num * y_num
          lowerCAmelCase_       :    Optional[int]								=			x_den * y_num + x_num * y_den
          lowerCAmelCase_       :    Any								=			gcd(lowerCAmelCase__   ,       lowerCAmelCase__						)
          z_num //= hcf
          z_den //= hcf
          if 0 < z_num < z_den <= order:
            lowerCAmelCase_       :    Tuple								=			add_three(
                lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__						)
            unique_s.add(lowerCAmelCase__						)

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

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

  return total.denominator + total.numerator


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










"""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


lowercase__		:    Tuple				   =     logging.get_logger(__name__)







class 				UpperCamelCase__       (     lowercase_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE      =					["""pixel_values"""]



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

        lowerCAmelCase_       :    List[Any]								=			do_resize
        lowerCAmelCase_       :    Any								=			do_rescale
        lowerCAmelCase_       :    int								=			do_normalize
        lowerCAmelCase_       :    List[str]								=			do_center_crop
        lowerCAmelCase_       :    Dict								=			crop_size
        lowerCAmelCase_       :    Optional[Any]								=			size
        lowerCAmelCase_       :    Tuple								=			resample
        lowerCAmelCase_       :    Optional[int]								=			rescale_factor
        lowerCAmelCase_       :    Optional[Any]								=			image_mean if image_mean is not None else IMAGENET_DEFAULT_MEAN
        lowerCAmelCase_       :    List[str]								=			image_std if image_std is not None else IMAGENET_DEFAULT_STD



      def 					SCREAMING_SNAKE_CASE__			(				self    :				Any   ,      SCREAMING_SNAKE_CASE_    :				np.ndarray   ,      SCREAMING_SNAKE_CASE_    :				Dict[str, int]   ,      SCREAMING_SNAKE_CASE_    :				PILImageResampling = PILImageResampling.BILINEAR   ,      SCREAMING_SNAKE_CASE_    :				Optional[Union[str, ChannelDimension]] = None   ,      **SCREAMING_SNAKE_CASE_    :				str   ,      ):
        lowerCAmelCase_       :    str								=			get_size_dict(SCREAMING_SNAKE_CASE_	)

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



      def 					SCREAMING_SNAKE_CASE__			(				self    :				Optional[int]   ,      SCREAMING_SNAKE_CASE_    :				np.ndarray   ,      SCREAMING_SNAKE_CASE_    :				Dict[str, int]   ,      SCREAMING_SNAKE_CASE_    :				Optional[Union[str, ChannelDimension]] = None   ,      **SCREAMING_SNAKE_CASE_    :				int   ,      ):
        lowerCAmelCase_       :    Any								=			get_size_dict(SCREAMING_SNAKE_CASE_	)
        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(SCREAMING_SNAKE_CASE_   ,      size=(size['height'], size['width'])   ,      data_format=SCREAMING_SNAKE_CASE_   ,      **SCREAMING_SNAKE_CASE_	)



      def 					SCREAMING_SNAKE_CASE__			(				self    :				int   ,      SCREAMING_SNAKE_CASE_    :				np.ndarray   ,      SCREAMING_SNAKE_CASE_    :				float   ,      SCREAMING_SNAKE_CASE_    :				Optional[Union[str, ChannelDimension]] = None   ,      **SCREAMING_SNAKE_CASE_    :				Optional[int]	):
        return rescale(SCREAMING_SNAKE_CASE_   ,      scale=SCREAMING_SNAKE_CASE_   ,      data_format=SCREAMING_SNAKE_CASE_   ,      **SCREAMING_SNAKE_CASE_	)



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





      def 					SCREAMING_SNAKE_CASE__			(				self    :				Tuple   ,      SCREAMING_SNAKE_CASE_    :				ImageInput   ,      SCREAMING_SNAKE_CASE_    :				Optional[bool] = None   ,      SCREAMING_SNAKE_CASE_    :				Dict[str, int] = None   ,      SCREAMING_SNAKE_CASE_    :				PILImageResampling = None   ,      SCREAMING_SNAKE_CASE_    :				bool = None   ,      SCREAMING_SNAKE_CASE_    :				int = None   ,      SCREAMING_SNAKE_CASE_    :				Optional[bool] = None   ,      SCREAMING_SNAKE_CASE_    :				Optional[float] = None   ,      SCREAMING_SNAKE_CASE_    :				Optional[bool] = None   ,      SCREAMING_SNAKE_CASE_    :				Optional[Union[float, List[float]]] = None   ,      SCREAMING_SNAKE_CASE_    :				Optional[Union[float, List[float]]] = None   ,      SCREAMING_SNAKE_CASE_    :				Optional[Union[str, TensorType]] = None   ,      SCREAMING_SNAKE_CASE_    :				Union[str, ChannelDimension] = ChannelDimension.FIRST   ,      **SCREAMING_SNAKE_CASE_    :				Optional[int]   ,      ):
        lowerCAmelCase_       :    Optional[int]								=			do_resize if do_resize is not None else self.do_resize
        lowerCAmelCase_       :    Optional[int]								=			do_rescale if do_rescale is not None else self.do_rescale
        lowerCAmelCase_       :    Optional[Any]								=			do_normalize if do_normalize is not None else self.do_normalize
        lowerCAmelCase_       :    Dict								=			do_center_crop if do_center_crop is not None else self.do_center_crop
        lowerCAmelCase_       :    Dict								=			crop_size if crop_size is not None else self.crop_size
        lowerCAmelCase_       :    Optional[Any]								=			get_size_dict(SCREAMING_SNAKE_CASE_   ,      param_name='crop_size'   ,      default_to_square=SCREAMING_SNAKE_CASE_	)
        lowerCAmelCase_       :    Union[str, Any]								=			resample if resample is not None else self.resample
        lowerCAmelCase_       :    Optional[Any]								=			rescale_factor if rescale_factor is not None else self.rescale_factor
        lowerCAmelCase_       :    str								=			image_mean if image_mean is not None else self.image_mean
        lowerCAmelCase_       :    List[str]								=			image_std if image_std is not None else self.image_std

        lowerCAmelCase_       :    Tuple								=			size if size is not None else self.size
        lowerCAmelCase_       :    str								=			get_size_dict(SCREAMING_SNAKE_CASE_	)

        if not is_batched(SCREAMING_SNAKE_CASE_	):
          lowerCAmelCase_       :    List[Any]								=			[images]

        if not valid_images(SCREAMING_SNAKE_CASE_	):
          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.
        lowerCAmelCase_       :    str								=			[to_numpy_array(SCREAMING_SNAKE_CASE_	) for image in images]

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

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

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

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

        lowerCAmelCase_       :    Any								=			[to_channel_dimension_format(SCREAMING_SNAKE_CASE_   ,      SCREAMING_SNAKE_CASE_	) for image in images]

        lowerCAmelCase_       :    Optional[Any]								=			{'pixel_values': images}
        return BatchFeature(data=SCREAMING_SNAKE_CASE_   ,      tensor_type=SCREAMING_SNAKE_CASE_	)





