
from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_speech_available, is_torch_available


_A   =			{
    "configuration_audio_spectrogram_transformer": [
        "AUDIO_SPECTROGRAM_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "ASTConfig",
    ]
}

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   _A   =			[
       "AUDIO_SPECTROGRAM_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
       "ASTForAudioClassification",
       "ASTModel",
       "ASTPreTrainedModel",
   ]

try:
   if not is_speech_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   _A   =			["ASTFeatureExtractor"]

if TYPE_CHECKING:
   from .configuration_audio_spectrogram_transformer import (
       AUDIO_SPECTROGRAM_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
       ASTConfig,
   )

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_audio_spectrogram_transformer import (
          AUDIO_SPECTROGRAM_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
          ASTForAudioClassification,
          ASTModel,
          ASTPreTrainedModel,
      )

   try:
      if not is_speech_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .feature_extraction_audio_spectrogram_transformer import ASTFeatureExtractor


else:
   import sys

   _A   =			_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)



from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt



def 						lowercase_      (       A__		)							->							bool:
    """simple docstring"""

    snake_case								= int(number**0.5		)
    return number == sq * sq



def 						lowercase_      (       A__			,		A__			,		A__			,		A__			,		A__			,		A__		)							->							tuple[int, int]:
    """simple docstring"""

    snake_case								= x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
    snake_case								= x_den * y_den * z_den
    snake_case								= gcd(A__			,		A__		)
    top //= hcf
    bottom //= hcf
    return top, bottom



def 						lowercase_      (       A__ = 35		)							->							int:
    """simple docstring"""

    snake_case								= set()
    snake_case								= 42
    snake_case								= Fraction(0		)
    snake_case								= 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
                    snake_case								= x_num * y_den + x_den * y_num
                    snake_case								= x_den * y_den
                    snake_case								= gcd(A__			,		A__		)
                    z_num //= hcf
                    z_den //= hcf
                    if 0 < z_num < z_den <= order:
                        snake_case								= add_three(
                            A__			,		A__			,		A__			,		A__			,		A__			,		A__		)
                        unique_s.add(A__		)

                    # n=2
                    snake_case								= (
                        x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
                    )
                    snake_case								= x_den * x_den * y_den * y_den
                    if is_sq(A__		) and is_sq(A__		):
                        snake_case								= int(sqrt(A__		)		)
                        snake_case								= int(sqrt(A__		)		)
                        snake_case								= gcd(A__			,		A__		)
                        z_num //= hcf
                        z_den //= hcf
                        if 0 < z_num < z_den <= order:
                            snake_case								= add_three(
                                A__			,		A__			,		A__			,		A__			,		A__			,		A__		)
                            unique_s.add(A__		)

                    # n=-1
                    snake_case								= x_num * y_num
                    snake_case								= x_den * y_num + x_num * y_den
                    snake_case								= gcd(A__			,		A__		)
                    z_num //= hcf
                    z_den //= hcf
                    if 0 < z_num < z_den <= order:
                        snake_case								= add_three(
                            A__			,		A__			,		A__			,		A__			,		A__			,		A__		)
                        unique_s.add(A__		)

                    # n=2
                    snake_case								= x_num * x_num * y_num * y_num
                    snake_case								= (
                        x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
                    )
                    if is_sq(A__		) and is_sq(A__		):
                        snake_case								= int(sqrt(A__		)		)
                        snake_case								= int(sqrt(A__		)		)
                        snake_case								= gcd(A__			,		A__		)
                        z_num //= hcf
                        z_den //= hcf
                        if 0 < z_num < z_den <= order:
                            snake_case								= add_three(
                                A__			,		A__			,		A__			,		A__			,		A__			,		A__		)
                            unique_s.add(A__		)

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

    return total.denominator + total.numerator


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

