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() = }")






import os
import tempfile
from functools import partial
from unittest import TestCase
from unittest.mock import patch

import datasets
import datasets.config

from .utils import require_beam






class      __lowercase					(    datasets.BeamBasedBuilder    ):

						def        __a		(	self				:      Tuple   )							->		Tuple:


									'''simple docstring'''

									return datasets.DatasetInfo(
									    features=datasets.Features({'''content''': datasets.Value('''string'''   )}   )							,							supervised_keys=__lowerCamelCase							,							)

						def        __a		(	self				:      Union[str, Any]							,							__lowerCamelCase				:      Union[str, Any]							,							__lowerCamelCase				:      Tuple   )							->		int:


									'''simple docstring'''

									return [datasets.SplitGenerator(name=datasets.Split.TRAIN							,							gen_kwargs={'''examples''': get_test_dummy_examples()}   )]



						def        __a		(	self				:      List[Any]							,							__lowerCamelCase				:      Any							,							__lowerCamelCase				:      Union[str, Any]   )							->		Optional[int]:


									'''simple docstring'''

									import apache_beam as beam

									return pipeline | "Load Examples" >> beam.Create(__lowerCamelCase   )






class      __lowercase					(    datasets.BeamBasedBuilder    ):

						def        __a		(	self				:      int   )							->		Any:


									'''simple docstring'''

									return datasets.DatasetInfo(
									    features=datasets.Features({'''a''': datasets.Sequence({'''b''': datasets.Value('''string'''   )}   )}   )							,							supervised_keys=__lowerCamelCase							,							)

						def        __a		(	self				:      Optional[int]							,							__lowerCamelCase				:      List[Any]							,							__lowerCamelCase				:      Optional[int]   )							->		int:


									'''simple docstring'''

									return [
									    datasets.SplitGenerator(name=datasets.Split.TRAIN							,							gen_kwargs={'''examples''': get_test_nested_examples()}   )
									]



						def        __a		(	self				:      Union[str, Any]							,							__lowerCamelCase				:      Tuple							,							__lowerCamelCase				:      Union[str, Any]   )							->		Tuple:


									'''simple docstring'''

									import apache_beam as beam

									return pipeline | "Load Examples" >> beam.Create(__lowerCamelCase   )






def        __UpperCAmelCase    (       )->       Dict:



			"""simple docstring"""







			return [(i, {"content": content}) for i, content in enumerate(['''foo''', '''bar''', '''foobar''']       )]






def        __UpperCAmelCase    (       )->       List[str]:



			"""simple docstring"""







			return [(i, {"a": {"b": [content]}}) for i, content in enumerate(['''foo''', '''bar''', '''foobar''']       )]






class      __lowercase					(    _A    ):

						@require_beam
						def        __a		(	self				:      Optional[int]   )							->		Optional[Any]:


									'''simple docstring'''

									lowercase							=		len(get_test_dummy_examples()   )
									with tempfile.TemporaryDirectory() as tmp_cache_dir:
												lowercase							=		DummyBeamDataset(cache_dir=__lowerCamelCase							,							beam_runner='''DirectRunner'''   )
												builder.download_and_prepare()
												self.assertTrue(
												    os.path.exists(
												        os.path.join(__lowerCamelCase							,							builder.name							,							'''default'''							,							'''0.0.0'''							,							f'{builder.name}-train.arrow'   )   )   )
												self.assertDictEqual(builder.info.features							,							datasets.Features({'''content''': datasets.Value('''string'''   )}   )   )
												lowercase							=		builder.as_dataset()
												self.assertEqual(dset['''train'''].num_rows							,							__lowerCamelCase   )
												self.assertEqual(dset['''train'''].info.splits['''train'''].num_examples							,							__lowerCamelCase   )
												self.assertDictEqual(dset['''train'''][0]							,							get_test_dummy_examples()[0][1]   )
												self.assertDictEqual(
												    dset['''train'''][expected_num_examples - 1]							,							get_test_dummy_examples()[expected_num_examples - 1][1]   )
												self.assertTrue(
												    os.path.exists(os.path.join(__lowerCamelCase							,							builder.name							,							'''default'''							,							'''0.0.0'''							,							'''dataset_info.json'''   )   )   )
												del dset

						@require_beam
						def        __a		(	self				:      Union[str, Any]   )							->		List[Any]:


									'''simple docstring'''

									import apache_beam as beam

									lowercase							=		beam.io.parquetio.WriteToParquet

									lowercase							=		len(get_test_dummy_examples()   )
									with tempfile.TemporaryDirectory() as tmp_cache_dir:
												lowercase							=		DummyBeamDataset(cache_dir=__lowerCamelCase							,							beam_runner='''DirectRunner'''   )
												with patch('''apache_beam.io.parquetio.WriteToParquet'''   ) as write_parquet_mock:
															lowercase							=		partial(__lowerCamelCase							,							num_shards=2   )
															builder.download_and_prepare()
												self.assertTrue(
												    os.path.exists(
												        os.path.join(
												            __lowerCamelCase							,							builder.name							,							'''default'''							,							'''0.0.0'''							,							f'{builder.name}-train-00000-of-00002.arrow'   )   )   )
												self.assertTrue(
												    os.path.exists(
												        os.path.join(
												            __lowerCamelCase							,							builder.name							,							'''default'''							,							'''0.0.0'''							,							f'{builder.name}-train-00000-of-00002.arrow'   )   )   )
												self.assertDictEqual(builder.info.features							,							datasets.Features({'''content''': datasets.Value('''string'''   )}   )   )
												lowercase							=		builder.as_dataset()
												self.assertEqual(dset['''train'''].num_rows							,							__lowerCamelCase   )
												self.assertEqual(dset['''train'''].info.splits['''train'''].num_examples							,							__lowerCamelCase   )
												# Order is not preserved when sharding, so we just check that all the elements are there
												self.assertListEqual(sorted(dset['''train''']['''content''']   )							,							sorted(['''foo''', '''bar''', '''foobar''']   )   )
												self.assertTrue(
												    os.path.exists(os.path.join(__lowerCamelCase							,							builder.name							,							'''default'''							,							'''0.0.0'''							,							'''dataset_info.json'''   )   )   )
												del dset

						@require_beam
						def        __a		(	self				:      int   )							->		int:


									'''simple docstring'''

									with tempfile.TemporaryDirectory() as tmp_cache_dir:
												lowercase							=		DummyBeamDataset(cache_dir=__lowerCamelCase   )
												self.assertRaises(datasets.builder.MissingBeamOptions							,							builder.download_and_prepare   )



						@require_beam
						def        __a		(	self				:      str   )							->		List[Any]:


									'''simple docstring'''

									lowercase							=		len(get_test_nested_examples()   )
									with tempfile.TemporaryDirectory() as tmp_cache_dir:
												lowercase							=		NestedBeamDataset(cache_dir=__lowerCamelCase							,							beam_runner='''DirectRunner'''   )
												builder.download_and_prepare()
												self.assertTrue(
												    os.path.exists(
												        os.path.join(__lowerCamelCase							,							builder.name							,							'''default'''							,							'''0.0.0'''							,							f'{builder.name}-train.arrow'   )   )   )
												self.assertDictEqual(
												    builder.info.features							,							datasets.Features({'''a''': datasets.Sequence({'''b''': datasets.Value('''string'''   )}   )}   )   )
												lowercase							=		builder.as_dataset()
												self.assertEqual(dset['''train'''].num_rows							,							__lowerCamelCase   )
												self.assertEqual(dset['''train'''].info.splits['''train'''].num_examples							,							__lowerCamelCase   )
												self.assertDictEqual(dset['''train'''][0]							,							get_test_nested_examples()[0][1]   )
												self.assertDictEqual(
												    dset['''train'''][expected_num_examples - 1]							,							get_test_nested_examples()[expected_num_examples - 1][1]   )
												self.assertTrue(
												    os.path.exists(os.path.join(__lowerCamelCase							,							builder.name							,							'''default'''							,							'''0.0.0'''							,							'''dataset_info.json'''   )   )   )
												del dset





