


'''simple docstring'''

from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt





def lowerCamelCase      (      lowerCAmelCase    :     int		) ->    bool:





	"""simple docstring"""







	__magic_name__	:   Any					     =					int(number**0.5		)
	return number == sq * sq





def lowerCamelCase      (      lowerCAmelCase    :     int		,		lowerCAmelCase    :     int		,		lowerCAmelCase    :     int		,		lowerCAmelCase    :     int		,		lowerCAmelCase    :     int		,		lowerCAmelCase    :     int		) ->    tuple[int, int]:





	"""simple docstring"""







	__magic_name__	:   str					     =					x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
	__magic_name__	:   List[str]					     =					x_den * y_den * z_den
	__magic_name__	:   Any					     =					gcd(SCREAMING_SNAKE_CASE_		,		SCREAMING_SNAKE_CASE_		)
	top //= hcf
	bottom //= hcf
	return top, bottom





def lowerCamelCase      (      lowerCAmelCase    :     int = 35		) ->    int:





	"""simple docstring"""







	__magic_name__	:   Union[str, Any]					     =					set()
	__magic_name__	:   Tuple					     =					42
	__magic_name__	:   str					     =					Fraction(0		)
	__magic_name__	:   Any					     =					42

	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
					__magic_name__	:   Union[str, Any]					     =					x_num * y_den + x_den * y_num
					__magic_name__	:   str					     =					x_den * y_den
					__magic_name__	:   Tuple					     =					gcd(SCREAMING_SNAKE_CASE_		,		SCREAMING_SNAKE_CASE_		)
					z_num //= hcf
					z_den //= hcf
					if 0 < z_num < z_den <= order:
						__magic_name__	:   Union[str, Any]					     =					add_three(
						    SCREAMING_SNAKE_CASE_		,		SCREAMING_SNAKE_CASE_		,		SCREAMING_SNAKE_CASE_		,		SCREAMING_SNAKE_CASE_		,		SCREAMING_SNAKE_CASE_		,		SCREAMING_SNAKE_CASE_		)
						unique_s.add(SCREAMING_SNAKE_CASE_		)

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

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

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

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

	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_STANDARD_MEAN,
    IMAGENET_STANDARD_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, logging


lowerCAmelCase				:Tuple        =      logging.get_logger(__name__)
class _lowerCamelCase	(						lowercase__							):



		'''simple docstring'''







		A_     :      int				   =    ["""pixel_values"""]







		def __init__( self		:						Any  ,					_A		:						bool = True  ,					_A		:						Optional[Dict[str, int]] = None  ,					_A		:						PILImageResampling = PILImageResampling.BILINEAR  ,					_A		:						bool = True  ,					_A		:						Dict[str, int] = None  ,					_A		:						bool = True  ,					_A		:						Union[int, float] = 1 / 255  ,					_A		:						bool = True  ,					_A		:						Optional[Union[float, List[float]]] = None  ,					_A		:						Optional[Union[float, List[float]]] = None  ,					**_A		:						Optional[Any]  ,					)  ->			None:
			super().__init__(**_A      )
			__magic_name__	:   List[str]					     =					size if size is not None else {'shortest_edge': 256}
			__magic_name__	:   str					     =					get_size_dict(_A  ,					default_to_square=_A      )
			__magic_name__	:   List[str]					     =					crop_size if crop_size is not None else {'height': 224, 'width': 224}
			__magic_name__	:   Optional[int]					     =					get_size_dict(_A      )
			__magic_name__	:   Union[str, Any]					     =					do_resize
			__magic_name__	:   List[Any]					     =					size
			__magic_name__	:   List[str]					     =					resample
			__magic_name__	:   Dict					     =					do_center_crop
			__magic_name__	:   List[str]					     =					crop_size
			__magic_name__	:   int					     =					do_rescale
			__magic_name__	:   Tuple					     =					rescale_factor
			__magic_name__	:   List[str]					     =					do_normalize
			__magic_name__	:   Union[str, Any]					     =					image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
			__magic_name__	:   Dict					     =					image_std if image_std is not None else IMAGENET_STANDARD_STD







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







		def        __lowerCAmelCase		( self		:						Dict  ,					_A		:						np.ndarray  ,					_A		:						Dict[str, int]  ,					_A		:						Optional[Union[str, ChannelDimension]] = None  ,					**_A		:						Optional[int]  ,					)  ->			np.ndarray:
			__magic_name__	:   int					     =					get_size_dict(_A      )
			return center_crop(_A  ,					size=(size['height'], size['width'])  ,					data_format=_A  ,					**_A      )







		def        __lowerCAmelCase		( self		:						List[str]  ,					_A		:						np.ndarray  ,					_A		:						float  ,					_A		:						Optional[Union[str, ChannelDimension]] = None  ,					**_A		:						Tuple      )  ->			np.ndarray:
			return rescale(_A  ,					scale=_A  ,					data_format=_A  ,					**_A      )







		def        __lowerCAmelCase		( self		:						str  ,					_A		:						np.ndarray  ,					_A		:						Union[float, List[float]]  ,					_A		:						Union[float, List[float]]  ,					_A		:						Optional[Union[str, ChannelDimension]] = None  ,					**_A		:						int  ,					)  ->			np.ndarray:
			return normalize(_A  ,					mean=_A  ,					std=_A  ,					data_format=_A  ,					**_A      )







		def        __lowerCAmelCase		( self		:						List[str]  ,					_A		:						ImageInput  ,					_A		:						Optional[bool] = None  ,					_A		:						Dict[str, int] = None  ,					_A		:						PILImageResampling = None  ,					_A		:						bool = None  ,					_A		:						Dict[str, int] = None  ,					_A		:						Optional[bool] = None  ,					_A		:						Optional[float] = None  ,					_A		:						Optional[bool] = None  ,					_A		:						Optional[Union[float, List[float]]] = None  ,					_A		:						Optional[Union[float, List[float]]] = None  ,					_A		:						Optional[Union[str, TensorType]] = None  ,					_A		:						Union[str, ChannelDimension] = ChannelDimension.FIRST  ,					**_A		:						List[Any]  ,					)  ->			List[str]:
			__magic_name__	:   int					     =					do_resize if do_resize is not None else self.do_resize
			__magic_name__	:   Tuple					     =					size if size is not None else self.size
			__magic_name__	:   Optional[Any]					     =					get_size_dict(_A  ,					default_to_square=_A      )
			__magic_name__	:   Dict					     =					resample if resample is not None else self.resample
			__magic_name__	:   Optional[Any]					     =					do_center_crop if do_center_crop is not None else self.do_center_crop
			__magic_name__	:   Dict					     =					crop_size if crop_size is not None else self.crop_size
			__magic_name__	:   List[str]					     =					get_size_dict(_A      )
			__magic_name__	:   Union[str, Any]					     =					do_rescale if do_rescale is not None else self.do_rescale
			__magic_name__	:   str					     =					rescale_factor if rescale_factor is not None else self.rescale_factor
			__magic_name__	:   Any					     =					do_normalize if do_normalize is not None else self.do_normalize
			__magic_name__	:   Tuple					     =					image_mean if image_mean is not None else self.image_mean
			__magic_name__	:   Union[str, Any]					     =					image_std if image_std is not None else self.image_std

			__magic_name__	:   int					     =					make_list_of_images(_A      )

			if not valid_images(_A      ):
				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.'      )

			# All transformations expect numpy arrays.
			__magic_name__	:   List[Any]					     =					[to_numpy_array(_A      ) for image in images]

			if do_resize:
				__magic_name__	:   Union[str, Any]					     =					[self.resize(image=_A  ,					size=_A  ,					resample=_A      ) for image in images]

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

			if do_rescale:
				__magic_name__	:   List[Any]					     =					[self.rescale(image=_A  ,					scale=_A      ) for image in images]

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

			__magic_name__	:   Union[str, Any]					     =					[to_channel_dimension_format(_A  ,					_A      ) for image in images]

			__magic_name__	:   List[str]					     =					{'pixel_values': images}
			return BatchFeature(data=_A  ,					tensor_type=_A      )