


from typing import TYPE_CHECKING

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


__lowerCamelCase        =     {"configuration_mbart": ["MBART_PRETRAINED_CONFIG_ARCHIVE_MAP", "MBartConfig", "MBartOnnxConfig"]}

try:
    if not is_sentencepiece_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __lowerCamelCase        =     ["MBartTokenizer"]

try:
    if not is_tokenizers_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __lowerCamelCase        =     ["MBartTokenizerFast"]

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __lowerCamelCase        =     [
        "MBART_PRETRAINED_MODEL_ARCHIVE_LIST",
        "MBartForCausalLM",
        "MBartForConditionalGeneration",
        "MBartForQuestionAnswering",
        "MBartForSequenceClassification",
        "MBartModel",
        "MBartPreTrainedModel",
    ]

try:
    if not is_tf_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __lowerCamelCase        =     [
        "TFMBartForConditionalGeneration",
        "TFMBartModel",
        "TFMBartPreTrainedModel",
    ]

try:
    if not is_flax_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __lowerCamelCase        =     [
        "FlaxMBartForConditionalGeneration",
        "FlaxMBartForQuestionAnswering",
        "FlaxMBartForSequenceClassification",
        "FlaxMBartModel",
        "FlaxMBartPreTrainedModel",
    ]


if TYPE_CHECKING:
    from .configuration_mbart import MBART_PRETRAINED_CONFIG_ARCHIVE_MAP, MBartConfig, MBartOnnxConfig

    try:
        if not is_sentencepiece_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .tokenization_mbart import MBartTokenizer

    try:
        if not is_tokenizers_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .tokenization_mbart_fast import MBartTokenizerFast

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_mbart import (
            MBART_PRETRAINED_MODEL_ARCHIVE_LIST,
            MBartForCausalLM,
            MBartForConditionalGeneration,
            MBartForQuestionAnswering,
            MBartForSequenceClassification,
            MBartModel,
            MBartPreTrainedModel,
        )

    try:
        if not is_tf_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_tf_mbart import TFMBartForConditionalGeneration, TFMBartModel, TFMBartPreTrainedModel

    try:
        if not is_flax_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_flax_mbart import (
            FlaxMBartForConditionalGeneration,
            FlaxMBartForQuestionAnswering,
            FlaxMBartForSequenceClassification,
            FlaxMBartModel,
            FlaxMBartPreTrainedModel,
        )

else:
    import sys

    __lowerCamelCase        =     _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)







from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt



def  _a			(						__UpperCamelCase ):
     a_    :     int										=    int(number**0.5 )
     return number == sq * sq



def  _a			(						__UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase ):
     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(__UpperCamelCase  ,  __UpperCamelCase )
     top //= hcf
     bottom //= hcf
     return top, bottom



def  _a			(						__UpperCamelCase = 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_    :     int										=    x_num * y_den + x_den * y_num
                         a_    :     Optional[int]										=    x_den * y_den
                         a_    :     Optional[Any]										=    gcd(__UpperCamelCase  ,  __UpperCamelCase )
                         z_num //= hcf
                         z_den //= hcf
                         if 0 < z_num < z_den <= order:
                              a_    :     Optional[int]										=    add_three(
                                  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase )
                              unique_s.add(__UpperCamelCase )

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

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

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

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

     return total.denominator + total.numerator


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



