from typing import TYPE_CHECKING

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


A_      =      {
    "configuration_transfo_xl": ["TRANSFO_XL_PRETRAINED_CONFIG_ARCHIVE_MAP", "TransfoXLConfig"],
    "tokenization_transfo_xl": ["TransfoXLCorpus", "TransfoXLTokenizer"],
}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A_      =      [
						    "TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST",
						    "AdaptiveEmbedding",
						    "TransfoXLForSequenceClassification",
						    "TransfoXLLMHeadModel",
						    "TransfoXLModel",
						    "TransfoXLPreTrainedModel",
						    "load_tf_weights_in_transfo_xl",
						]

try:
						if not is_tf_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A_      =      [
						    "TF_TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST",
						    "TFAdaptiveEmbedding",
						    "TFTransfoXLForSequenceClassification",
						    "TFTransfoXLLMHeadModel",
						    "TFTransfoXLMainLayer",
						    "TFTransfoXLModel",
						    "TFTransfoXLPreTrainedModel",
						]


if TYPE_CHECKING:
						from .configuration_transfo_xl import TRANSFO_XL_PRETRAINED_CONFIG_ARCHIVE_MAP, TransfoXLConfig
						from .tokenization_transfo_xl import TransfoXLCorpus, TransfoXLTokenizer

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_transfo_xl import (
												    TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST,
												    AdaptiveEmbedding,
												    TransfoXLForSequenceClassification,
												    TransfoXLLMHeadModel,
												    TransfoXLModel,
												    TransfoXLPreTrainedModel,
												    load_tf_weights_in_transfo_xl,
												)

						try:
												if not is_tf_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_tf_transfo_xl import (
												    TF_TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST,
												    TFAdaptiveEmbedding,
												    TFTransfoXLForSequenceClassification,
												    TFTransfoXLLMHeadModel,
												    TFTransfoXLMainLayer,
												    TFTransfoXLModel,
												    TFTransfoXLPreTrainedModel,
												)

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        __UpperCAmelCase    (       UpperCAmelCase       )->       bool:



			"""simple docstring"""







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






def        __UpperCAmelCase    (       UpperCAmelCase,		UpperCAmelCase,		UpperCAmelCase,		UpperCAmelCase,		UpperCAmelCase,		UpperCAmelCase       )->       tuple[int, int]:



			"""simple docstring"""







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






def        __UpperCAmelCase    (       UpperCAmelCase = 35       )->       int:



			"""simple docstring"""







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

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

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

															# n=2
															lowercase							=		x_num * x_num * y_num * y_num
															lowercase							=		(
															    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
															)
															if is_sq(UpperCAmelCase       ) and is_sq(UpperCAmelCase       ):
																		lowercase							=		int(sqrt(UpperCAmelCase       )       )
																		lowercase							=		int(sqrt(UpperCAmelCase       )       )
																		lowercase							=		gcd(UpperCAmelCase,		UpperCAmelCase       )
																		z_num //= hcf
																		z_den //= hcf
																		if 0 < z_num < z_den <= order:
																					lowercase							=		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() = }")





