import importlib
import os
import sys


# This is required to make the module import works (when the python process is running from the root of the repo)
sys.path.append(".")






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Optional[int]:



			"""simple docstring"""







			lowercase							=		test_file.split(os.path.sep       )
			if components[0:2] != ["tests", "models"]:
						raise ValueError(
						    '''`test_file` should start with `tests/models/` (with `/` being the OS specific path separator). Got '''
						    f'{test_file} instead.'       )
			lowercase							=		components[-1]
			if not test_fn.endswith('''py'''       ):
						raise ValueError(f'`test_file` should be a python file. Got {test_fn} instead.'       )
			if not test_fn.startswith('''test_modeling_'''       ):
						raise ValueError(
						    f'`test_file` should point to a file name of the form `test_modeling_*.py`. Got {test_fn} instead.'       )

			lowercase							=		components[:-1] + [test_fn.replace('''.py''',		''''''       )]
			lowercase							=		'''.'''.join(UpperCAmelCase       )

			return test_module_path






def        __UpperCAmelCase    (       UpperCAmelCase       )->       List[Any]:



			"""simple docstring"""







			lowercase							=		get_module_path(UpperCAmelCase       )
			lowercase							=		importlib.import_module(UpperCAmelCase       )

			return test_module






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Optional[int]:



			"""simple docstring"""







			lowercase							=		[]
			lowercase							=		get_test_module(UpperCAmelCase       )
			for attr in dir(UpperCAmelCase       ):
						if attr.endswith('''ModelTester'''       ):
									tester_classes.append(getattr(UpperCAmelCase,		UpperCAmelCase       )       )

    # sort with class names
			return sorted(UpperCAmelCase,		key=lambda UpperCAmelCase       : x.__name__       )






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Optional[int]:



			"""simple docstring"""







			lowercase							=		[]
			lowercase							=		get_test_module(UpperCAmelCase       )
			for attr in dir(UpperCAmelCase       ):
						lowercase							=		getattr(UpperCAmelCase,		UpperCAmelCase       )
						# (TF/Flax)ModelTesterMixin is also an attribute in specific model test module. Let's exclude them by checking
						# `all_model_classes` is not empty (which also excludes other special classes).
						lowercase							=		getattr(UpperCAmelCase,		'''all_model_classes''',		[]       )
						if len(UpperCAmelCase       ) > 0:
									test_classes.append(UpperCAmelCase       )

    # sort with class names
			return sorted(UpperCAmelCase,		key=lambda UpperCAmelCase       : x.__name__       )






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Any:



			"""simple docstring"""







			lowercase							=		get_test_classes(UpperCAmelCase       )
			lowercase							=		set()
			for test_class in test_classes:
						model_classes.update(test_class.all_model_classes       )

			# sort with class names
			return sorted(UpperCAmelCase,		key=lambda UpperCAmelCase       : x.__name__       )






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Optional[int]:



			"""simple docstring"""







			lowercase							=		test_class()
			if hasattr(UpperCAmelCase,		'''setUp'''       ):
						test.setUp()

			lowercase							=		None
			if hasattr(UpperCAmelCase,		'''model_tester'''       ):
						# `(TF/Flax)ModelTesterMixin` has this attribute default to `None`. Let's skip this case.
						if test.model_tester is not None:
									lowercase							=		test.model_tester.__class__

			return model_tester






def        __UpperCAmelCase    (       UpperCAmelCase,		UpperCAmelCase       )->       Optional[Any]:



			"""simple docstring"""







			lowercase							=		get_test_classes(UpperCAmelCase       )

			lowercase							=		[]
			for test_class in test_classes:
						if model_class in test_class.all_model_classes:
									target_test_classes.append(UpperCAmelCase       )

    # sort with class names
			return sorted(UpperCAmelCase,		key=lambda UpperCAmelCase       : x.__name__       )






def        __UpperCAmelCase    (       UpperCAmelCase,		UpperCAmelCase       )->       Union[str, Any]:



			"""simple docstring"""







			lowercase							=		get_test_classes_for_model(UpperCAmelCase,		UpperCAmelCase       )

			lowercase							=		[]
			for test_class in test_classes:
						lowercase							=		get_model_tester_from_test_class(UpperCAmelCase       )
						if tester_class is not None:
									tester_classes.append(UpperCAmelCase       )

    # sort with class names
			return sorted(UpperCAmelCase,		key=lambda UpperCAmelCase       : x.__name__       )






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Dict:



			"""simple docstring"""







			lowercase							=		get_test_classes(UpperCAmelCase       )
			lowercase							=		{test_class: get_model_tester_from_test_class(UpperCAmelCase       ) for test_class in test_classes}
			return test_tester_mapping






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Union[str, Any]:



			"""simple docstring"""







			lowercase							=		get_model_classes(UpperCAmelCase       )
			lowercase							=		{
			    model_class: get_test_classes_for_model(UpperCAmelCase,		UpperCAmelCase       ) for model_class in model_classes
			}
			return model_test_mapping






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Any:



			"""simple docstring"""







			lowercase							=		get_model_classes(UpperCAmelCase       )
			lowercase							=		{
			    model_class: get_tester_classes_for_model(UpperCAmelCase,		UpperCAmelCase       ) for model_class in model_classes
			}
			return model_to_tester_mapping






def        __UpperCAmelCase    (       UpperCAmelCase       )->       Any:



			"""simple docstring"""







			if isinstance(UpperCAmelCase,		UpperCAmelCase       ):
						return o
			elif isinstance(UpperCAmelCase,		UpperCAmelCase       ):
						return o.__name__
			elif isinstance(UpperCAmelCase,		(list, tuple)       ):
						return [to_json(UpperCAmelCase       ) for x in o]
			elif isinstance(UpperCAmelCase,		UpperCAmelCase       ):
						return {to_json(UpperCAmelCase       ): to_json(UpperCAmelCase       ) for k, v in o.items()}
			else:
						return o






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() = }")





