



def      __snake_case	(			_UpperCAmelCase				):
    assert isinstance(_lowerCAmelCase   , _lowerCAmelCase				), f'The input value of [n={number}] is not an integer'

    if number == 1:
        return 2
    elif number < 1:
        __a						       =				f'The input value of [n={number}] has to be > 0'
        raise ValueError(_lowerCAmelCase				)
    else:
        __a						       =				sylvester(number - 1				)
        __a						       =				num - 1
        __a						       =				num
        return lower * upper + 1


if __name__ == "__main__":
 print(f'The 8th number in Sylvester\'s sequence: {sylvester(8)}')










'''simple docstring'''






import tempfile
import unittest

import numpy as np
from huggingface_hub import HfFolder, delete_repo
from requests.exceptions import HTTPError

from transformers import BertConfig, is_flax_available
from transformers.testing_utils import TOKEN, USER, is_staging_test, require_flax


if is_flax_available():
						import os

						from flax.core.frozen_dict import unfreeze
						from flax.traverse_util import flatten_dict

						from transformers import FlaxBertModel

						UpperCamelCase__:   Tuple								=			"0.12"  # assumed parallelism: 8

@require_flax
@is_staging_test
class 				SCREAMING_SNAKE_CASE(							unittest.TestCase			):







	"""simple docstring"""






	@classmethod
	def      A	(						cls			:     Union[str, Any]		)			->		int:
								UpperCAmelCase :       Optional[Any] 							=		TOKEN
								HfFolder.save_token(__snake_case		)







	@classmethod
	def      A	(						cls			:     List[str]		)			->		Tuple:
								try:
															delete_repo(token=cls._token		,			repo_id='''test-model-flax'''		)
								except HTTPError:
															pass

								try:
															delete_repo(token=cls._token		,			repo_id='''valid_org/test-model-flax-org'''		)
								except HTTPError:
															pass







	def      A	(						self			:     int		)			->		Tuple:
								UpperCAmelCase :       List[Any] 							=		BertConfig(
								    vocab_size=99		,			hidden_size=32		,			num_hidden_layers=5		,			num_attention_heads=4		,			intermediate_size=37		)
								UpperCAmelCase :       Dict 							=		FlaxBertModel(__snake_case		)
								model.push_to_hub('''test-model-flax'''		,			use_auth_token=self._token		)

								UpperCAmelCase :       Tuple 							=		FlaxBertModel.from_pretrained(F"""{USER}/test-model-flax"""		)

								UpperCAmelCase :       List[Any] 							=		flatten_dict(unfreeze(model.params		)		)
								UpperCAmelCase :       Tuple 							=		flatten_dict(unfreeze(new_model.params		)		)

								for key in base_params.keys():
															UpperCAmelCase :       Union[str, Any] 							=		(base_params[key] - new_params[key]).sum().item()
															self.assertLessEqual(__snake_case		,			1E-3		,			msg=F"""{key} not identical"""		)

								# Reset repo
								delete_repo(token=self._token		,			repo_id='''test-model-flax'''		)

								# Push to hub via save_pretrained
								with tempfile.TemporaryDirectory() as tmp_dir:
															model.save_pretrained(__snake_case		,			repo_id='''test-model-flax'''		,			push_to_hub=__snake_case		,			use_auth_token=self._token		)

								UpperCAmelCase :       str 							=		FlaxBertModel.from_pretrained(F"""{USER}/test-model-flax"""		)

								UpperCAmelCase :       Any 							=		flatten_dict(unfreeze(model.params		)		)
								UpperCAmelCase :       str 							=		flatten_dict(unfreeze(new_model.params		)		)

								for key in base_params.keys():
															UpperCAmelCase :       Optional[Any] 							=		(base_params[key] - new_params[key]).sum().item()
															self.assertLessEqual(__snake_case		,			1E-3		,			msg=F"""{key} not identical"""		)







	def      A	(						self			:     Optional[Any]		)			->		Union[str, Any]:
								UpperCAmelCase :       Dict 							=		BertConfig(
								    vocab_size=99		,			hidden_size=32		,			num_hidden_layers=5		,			num_attention_heads=4		,			intermediate_size=37		)
								UpperCAmelCase :       Optional[Any] 							=		FlaxBertModel(__snake_case		)
								model.push_to_hub('''valid_org/test-model-flax-org'''		,			use_auth_token=self._token		)

								UpperCAmelCase :       Union[str, Any] 							=		FlaxBertModel.from_pretrained('''valid_org/test-model-flax-org'''		)

								UpperCAmelCase :       List[Any] 							=		flatten_dict(unfreeze(model.params		)		)
								UpperCAmelCase :       int 							=		flatten_dict(unfreeze(new_model.params		)		)

								for key in base_params.keys():
															UpperCAmelCase :       Any 							=		(base_params[key] - new_params[key]).sum().item()
															self.assertLessEqual(__snake_case		,			1E-3		,			msg=F"""{key} not identical"""		)

								# Reset repo
								delete_repo(token=self._token		,			repo_id='''valid_org/test-model-flax-org'''		)

								# Push to hub via save_pretrained
								with tempfile.TemporaryDirectory() as tmp_dir:
															model.save_pretrained(
															    __snake_case		,			repo_id='''valid_org/test-model-flax-org'''		,			push_to_hub=__snake_case		,			use_auth_token=self._token		)

								UpperCAmelCase :       str 							=		FlaxBertModel.from_pretrained('''valid_org/test-model-flax-org'''		)

								UpperCAmelCase :       Any 							=		flatten_dict(unfreeze(model.params		)		)
								UpperCAmelCase :       Optional[Any] 							=		flatten_dict(unfreeze(new_model.params		)		)

								for key in base_params.keys():
															UpperCAmelCase :       int 							=		(base_params[key] - new_params[key]).sum().item()
															self.assertLessEqual(__snake_case		,			1E-3		,			msg=F"""{key} not identical"""		)


def  snake_case_     (					_lowerCAmelCase  :						Optional[Any]   ,      _lowerCAmelCase  :						Any  )      ->   Union[str, Any]:
							UpperCAmelCase :       str 							=		True
							UpperCAmelCase :       int 							=		flatten_dict(modela.params  )
							UpperCAmelCase :       Dict 							=		flatten_dict(modela.params  )
							for key in flat_params_a.keys():
														if np.sum(np.abs(flat_params_a[key] - flat_params_a[key]  )  ) > 1e-4:
																					UpperCAmelCase :       Dict 							=		False

							return models_are_equal




@require_flax
class 				SCREAMING_SNAKE_CASE(							unittest.TestCase			):







	"""simple docstring"""






	def      A	(						self			:     Tuple		)			->		Union[str, Any]:
								UpperCAmelCase :       List[Any] 							=		BertConfig.from_pretrained('''hf-internal-testing/tiny-bert-flax-only'''		)
								UpperCAmelCase :       Dict 							=		FlaxBertModel(__snake_case		)

								UpperCAmelCase :       int 							=		'''bert'''
								with tempfile.TemporaryDirectory() as tmp_dir:
															model.save_pretrained(os.path.join(__snake_case		,			__snake_case		)		)

															with self.assertRaises(__snake_case		):
																						UpperCAmelCase :       Tuple 							=		FlaxBertModel.from_pretrained(__snake_case		)

															UpperCAmelCase :       str 							=		FlaxBertModel.from_pretrained(__snake_case		,			subfolder=__snake_case		)

								self.assertTrue(check_models_equal(__snake_case		,			__snake_case		)		)







	def      A	(						self			:     List[str]		)			->		Dict:
								UpperCAmelCase :       Dict 							=		BertConfig.from_pretrained('''hf-internal-testing/tiny-bert-flax-only'''		)
								UpperCAmelCase :       Dict 							=		FlaxBertModel(__snake_case		)

								UpperCAmelCase :       Optional[int] 							=		'''bert'''
								with tempfile.TemporaryDirectory() as tmp_dir:
															model.save_pretrained(os.path.join(__snake_case		,			__snake_case		)		,			max_shard_size='''10KB'''		)

															with self.assertRaises(__snake_case		):
																						UpperCAmelCase :       Any 							=		FlaxBertModel.from_pretrained(__snake_case		)

															UpperCAmelCase :       Union[str, Any] 							=		FlaxBertModel.from_pretrained(__snake_case		,			subfolder=__snake_case		)

								self.assertTrue(check_models_equal(__snake_case		,			__snake_case		)		)







	def      A	(						self			:     Optional[int]		)			->		str:
								UpperCAmelCase :       Dict 							=		'''bert'''
								UpperCAmelCase :       int 							=		'''hf-internal-testing/tiny-random-bert-subfolder'''

								with self.assertRaises(__snake_case		):
															UpperCAmelCase :       Optional[Any] 							=		FlaxBertModel.from_pretrained(__snake_case		)

								UpperCAmelCase :       Tuple 							=		FlaxBertModel.from_pretrained(__snake_case		,			subfolder=__snake_case		)

								self.assertIsNotNone(__snake_case		)







	def      A	(						self			:     Dict		)			->		List[Any]:
								UpperCAmelCase :       Optional[int] 							=		'''bert'''
								UpperCAmelCase :       int 							=		'''hf-internal-testing/tiny-random-bert-sharded-subfolder'''
								with self.assertRaises(__snake_case		):
															UpperCAmelCase :       Dict 							=		FlaxBertModel.from_pretrained(__snake_case		)

								UpperCAmelCase :       Union[str, Any] 							=		FlaxBertModel.from_pretrained(__snake_case		,			subfolder=__snake_case		)

								self.assertIsNotNone(__snake_case		)





