



"""simple docstring"""
from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCAmelCase  :						Dict	=       {
    "configuration_longformer": [
        "LONGFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "LongformerConfig",
        "LongformerOnnxConfig",
    ],
    "tokenization_longformer": ["LongformerTokenizer"],
}

try:
       if not is_tokenizers_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       UpperCAmelCase  :						List[Any]	=       ["LongformerTokenizerFast"]

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       UpperCAmelCase  :						Optional[int]	=       [
           "LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
           "LongformerForMaskedLM",
           "LongformerForMultipleChoice",
           "LongformerForQuestionAnswering",
           "LongformerForSequenceClassification",
           "LongformerForTokenClassification",
           "LongformerModel",
           "LongformerPreTrainedModel",
           "LongformerSelfAttention",
       ]

try:
       if not is_tf_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       UpperCAmelCase  :						Optional[int]	=       [
           "TF_LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
           "TFLongformerForMaskedLM",
           "TFLongformerForMultipleChoice",
           "TFLongformerForQuestionAnswering",
           "TFLongformerForSequenceClassification",
           "TFLongformerForTokenClassification",
           "TFLongformerModel",
           "TFLongformerPreTrainedModel",
           "TFLongformerSelfAttention",
       ]


if TYPE_CHECKING:
       from .configuration_longformer import (
           LONGFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
           LongformerConfig,
           LongformerOnnxConfig,
       )
       from .tokenization_longformer import LongformerTokenizer

       try:
              if not is_tokenizers_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .tokenization_longformer_fast import LongformerTokenizerFast

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_longformer import (
                  LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
                  LongformerForMaskedLM,
                  LongformerForMultipleChoice,
                  LongformerForQuestionAnswering,
                  LongformerForSequenceClassification,
                  LongformerForTokenClassification,
                  LongformerModel,
                  LongformerPreTrainedModel,
                  LongformerSelfAttention,
              )

       try:
              if not is_tf_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_tf_longformer import (
                  TF_LONGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
                  TFLongformerForMaskedLM,
                  TFLongformerForMultipleChoice,
                  TFLongformerForQuestionAnswering,
                  TFLongformerForSequenceClassification,
                  TFLongformerForTokenClassification,
                  TFLongformerModel,
                  TFLongformerPreTrainedModel,
                  TFLongformerSelfAttention,
              )

else:
       import sys

       UpperCAmelCase  :						List[Any]	=       _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)



from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt




def    __UpperCamelCase     (				lowerCAmelCase__							:				int  ):
 __a :  int						=  int(number**0.5  )
 return number == sq * sq




def    __UpperCamelCase     (				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    __UpperCamelCase     (				lowerCAmelCase__							:				int = 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 :  Any						=  x_num * y_den + x_den * y_num
     __a :  Dict						=  x_den * y_den
     __a :  int						=  gcd(lowerCAmelCase__  ,   lowerCAmelCase__  )
     z_num //= hcf
     z_den //= hcf
     if 0 < z_num < z_den <= order:
      __a :  str						=  add_three(
          lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  )
      unique_s.add(lowerCAmelCase__  )

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

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

     # n=2
     __a :  List[str]						=  x_num * x_num * y_num * y_num
     __a :  Optional[int]						=  (
         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 :  Union[str, Any]						=  int(sqrt(lowerCAmelCase__  )  )
      __a :  List[str]						=  int(sqrt(lowerCAmelCase__  )  )
      __a :  Optional[int]						=  gcd(lowerCAmelCase__  ,   lowerCAmelCase__  )
      z_num //= hcf
      z_den //= hcf
      if 0 < z_num < z_den <= order:
       __a :  int						=  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() = }""")
