




"""simple docstring"""






from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt





def 							UpperCAmelCase		(		snake_case			:					int    ):
     _lowerCAmelCase:int									=  int(number**0.5    )
     return number == sq * sq





def 							UpperCAmelCase		(		snake_case			:					int      ,       snake_case			:					int      ,       snake_case			:					int      ,       snake_case			:					int      ,       snake_case			:					int      ,       snake_case			:					int    ):
     _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(snake_case      ,       snake_case    )
     top //= hcf
     bottom //= hcf
     return top, bottom





def 							UpperCAmelCase		(		snake_case			:					int = 35    ):
     _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:Any									=  x_num * y_den + x_den * y_num
                         _lowerCAmelCase:str									=  x_den * y_den
                         _lowerCAmelCase:List[Any]									=  gcd(snake_case      ,       snake_case    )
                         z_num //= hcf
                         z_den //= hcf
                         if 0 < z_num < z_den <= order:
                              _lowerCAmelCase:str									=  add_three(
                                  snake_case      ,       snake_case      ,       snake_case      ,       snake_case      ,       snake_case      ,       snake_case    )
                              unique_s.add(snake_case    )

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

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

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

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

     return total.denominator + total.numerator


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












"""simple docstring"""






from typing import List, Union

import numpy as np

from ..utils import add_end_docstrings, is_torch_available, is_vision_available, logging, requires_backends
from .base import PIPELINE_INIT_ARGS, Pipeline


if is_vision_available():
				from PIL import Image

				from ..image_utils import load_image

if is_torch_available():
				import torch

				from ..models.auto.modeling_auto import MODEL_FOR_DEPTH_ESTIMATION_MAPPING

UpperCamelCase__						=			logging.get_logger(__name__)




@add_end_docstrings(UpperCamelCase_  )
class   a__			(       UpperCamelCase_  ):





						def __init__(							self      :	int     ,*a__      :	Optional[Any]     ,**a__      :	Union[str, Any])						->       Tuple:




											"""simple docstring"""







											super().__init__(*a__     ,**a__)
											requires_backends(self     ,'''vision''')
											self.check_model_type(a__)





						def __call__(							self      :	str     ,a__      :	Union[str, List[str], "Image.Image", List["Image.Image"]]     ,**a__      :	List[str])						->       Optional[int]:




											"""simple docstring"""







											return super().__call__(a__     ,**a__)





						def       __UpperCamelCase     (							self      :	Union[str, Any]     ,**a__      :	List[Any])						->       Any:




											"""simple docstring"""







											return {}, {}, {}





						def       __UpperCamelCase     (							self      :	Tuple     ,a__      :	Optional[int])						->       Optional[Any]:




											"""simple docstring"""







											_lowerCAmelCase:List[str]									=  load_image(a__)
											_lowerCAmelCase:int									=  image.size
											_lowerCAmelCase:int									=  self.image_processor(images=a__     ,return_tensors=self.framework)
											return model_inputs





						def       __UpperCamelCase     (							self      :	Dict     ,a__      :	List[str])						->       Union[str, Any]:




											"""simple docstring"""







											_lowerCAmelCase:Any									=  self.model(**a__)
											return model_outputs







						def       __UpperCamelCase     (							self      :	List[Any]     ,a__      :	Dict)						->       Any:




											"""simple docstring"""







											_lowerCAmelCase:Optional[int]									=  model_outputs.predicted_depth
											_lowerCAmelCase:Union[str, Any]									=  torch.nn.functional.interpolate(
											    predicted_depth.unsqueeze(1)     ,size=self.image_size[::-1]     ,mode='''bicubic'''     ,align_corners=a__)
											_lowerCAmelCase:List[str]									=  prediction.squeeze().cpu().numpy()
											_lowerCAmelCase:Any									=  (output * 255 / np.max(a__)).astype('''uint8''')
											_lowerCAmelCase:Dict									=  Image.fromarray(a__)
											_lowerCAmelCase:Tuple									=  {}
											_lowerCAmelCase:Optional[int]									=  predicted_depth
											_lowerCAmelCase:str									=  depth
											return output_dict






