


'''simple docstring'''


from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt




def      lowerCamelCase					(      lowerCamelCase  :      int):
      A_						:  int          =				int(number**0.5)
      return number == sq * sq




def      lowerCamelCase					(      lowerCamelCase  :      int							,						lowerCamelCase  :      int							,						lowerCamelCase  :      int							,						lowerCamelCase  :      int							,						lowerCamelCase  :      int							,						lowerCamelCase  :      int):
      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(lowerCamelCase							,						lowerCamelCase)
      top //= hcf
      bottom //= hcf
      return top, bottom




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

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

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

                              # n=2
                              A_						:  str          =				x_num * x_num * y_num * y_num
                              A_						:  List[str]          =				(
                                  x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
                              )
                              if is_sq(lowerCamelCase) and is_sq(lowerCamelCase):
                                    A_						:  int          =				int(sqrt(lowerCamelCase))
                                    A_						:  List[Any]          =				int(sqrt(lowerCamelCase))
                                    A_						:  List[Any]          =				gcd(lowerCamelCase							,						lowerCamelCase)
                                    z_num //= hcf
                                    z_den //= hcf
                                    if 0 < z_num < z_den <= order:
                                          A_						:  Union[str, 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'''


import warnings
from typing import List, Optional, Union

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding, PaddingStrategy, PreTokenizedInput, TextInput, TruncationStrategy
from ...utils import TensorType



class 	__lowerCAmelCase		(							__SCREAMING_SNAKE_CASE    ):


  '''simple docstring'''







  a_  					=							["""image_processor""", """tokenizer"""]
  a_  					=							"""ViltImageProcessor"""
  a_  					=							("""BertTokenizer""", """BertTokenizerFast""")






  def __init__(							self :       List[Any]	,_a :       Optional[Any]=None	,_a :       List[str]=None	,**_a :       Any ):

        '''simple docstring'''




        A_						:  Any          =				None
        if "feature_extractor" in kwargs:
              warnings.warn(
                  """The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`"""
                  """ instead."""	,_a	,)
              A_						:  List[str]          =				kwargs.pop("""feature_extractor""" )

        A_						:  List[Any]          =				image_processor if image_processor is not None else feature_extractor
        if image_processor is None:
              raise ValueError("""You need to specify an `image_processor`.""" )
        if tokenizer is None:
              raise ValueError("""You need to specify a `tokenizer`.""" )

        super().__init__(_a	,_a )
        A_						:  Optional[Any]          =				self.image_processor






  def __call__(							self :       Any	,_a :       Tuple	,_a :       Union[TextInput, PreTokenizedInput, List[TextInput], List[PreTokenizedInput]] = None	,_a :       bool = True	,_a :       Union[bool, str, PaddingStrategy] = False	,_a :       Union[bool, str, TruncationStrategy] = None	,_a :       Optional[int] = None	,_a :       int = 0	,_a :       Optional[int] = None	,_a :       Optional[bool] = None	,_a :       Optional[bool] = None	,_a :       bool = False	,_a :       bool = False	,_a :       bool = False	,_a :       bool = False	,_a :       bool = True	,_a :       Optional[Union[str, TensorType]] = None	,**_a :       Tuple	,):

        '''simple docstring'''




        A_						:  int          =				self.tokenizer(
            text=_a	,add_special_tokens=_a	,padding=_a	,truncation=_a	,max_length=_a	,stride=_a	,pad_to_multiple_of=_a	,return_token_type_ids=_a	,return_attention_mask=_a	,return_overflowing_tokens=_a	,return_special_tokens_mask=_a	,return_offsets_mapping=_a	,return_length=_a	,verbose=_a	,return_tensors=_a	,**_a	,)
        # add pixel_values + pixel_mask
        A_						:  Optional[int]          =				self.image_processor(_a	,return_tensors=_a )
        encoding.update(_a )

        return encoding






  def        _a							(							self :       List[Any]	,*_a :       Any	,**_a :       Any ):

        '''simple docstring'''




        return self.tokenizer.batch_decode(*_a	,**_a )






  def        _a							(							self :       int	,*_a :       int	,**_a :       Optional[int] ):

        '''simple docstring'''




        return self.tokenizer.decode(*_a	,**_a )






  @property
  def        _a							(							self :       List[Any] ):

        '''simple docstring'''




        A_						:  Optional[int]          =				self.tokenizer.model_input_names
        A_						:  str          =				self.image_processor.model_input_names
        return list(dict.fromkeys(tokenizer_input_names + image_processor_input_names ) )






  @property
  def        _a							(							self :       str ):

        '''simple docstring'''




        warnings.warn(
            """`feature_extractor_class` is deprecated and will be removed in v5. Use `image_processor_class` instead."""	,_a	,)
        return self.image_processor_class






  @property
  def        _a							(							self :       int ):

        '''simple docstring'''




        warnings.warn(
            """`feature_extractor` is deprecated and will be removed in v5. Use `image_processor` instead."""	,_a	,)
        return self.image_processor
