



def      lowerCAmelCase__		(   lowerCamelCase_		:		int = 1000000):





				'''simple docstring'''

				lowerCAmelCase__					:    int												=					set(range(3	,lowerCamelCase_	,2))
				primes.add(2)
				for p in range(3	,lowerCamelCase_	,2):
								if p not in primes:
												continue
								primes.difference_update(set(range(p * p	,lowerCamelCase_	,lowerCamelCase_)))

				lowerCAmelCase__					:    int												=					[float(lowerCamelCase_) for n in range(limit + 1)]

				for p in primes:
								for n in range(lowerCamelCase_	,limit + 1	,lowerCamelCase_):
												phi[n] *= 1 - 1 / p

				return int(sum(phi[2:]))


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






import unittest

from transformers.models.xlm_prophetnet.tokenization_xlm_prophetnet import SPIECE_UNDERLINE, XLMProphetNetTokenizer
from transformers.testing_utils import get_tests_dir, require_sentencepiece, slow
from transformers.utils import cached_property

from ...test_tokenization_common import TokenizerTesterMixin


__snake_case    :		int  =get_tests_dir('fixtures/test_sentencepiece.model')



@require_sentencepiece
class 	lowerCamelCase__      (							lowerCamelCase__				,    unittest.TestCase):




		'''simple docstring'''



		snake_case_     =XLMProphetNetTokenizer
		snake_case_     =False
		snake_case_     =True



		def 		lowerCAmelCase__				(self			)					->      Tuple:

						"""simple docstring"""






						super().setUp()

						# We have a SentencePiece fixture for testing
						lowerCAmelCase__					:    int												=					XLMProphetNetTokenizer(__lowerCamelCase		,keep_accents=__lowerCamelCase			)
						tokenizer.save_pretrained(self.tmpdirname			)



		def 		lowerCAmelCase__				(self			)					->      Union[str, Any]:

						"""simple docstring"""






						lowerCAmelCase__					:    str												=					'''[PAD]'''
						lowerCAmelCase__					:    Tuple												=					0

						self.assertEqual(self.get_tokenizer()._convert_token_to_id(__lowerCamelCase			)		,__lowerCamelCase			)
						self.assertEqual(self.get_tokenizer()._convert_id_to_token(__lowerCamelCase			)		,__lowerCamelCase			)



		def 		lowerCAmelCase__				(self			)					->      Optional[Any]:

						"""simple docstring"""






						lowerCAmelCase__					:    Any												=					list(self.get_tokenizer().get_vocab().keys()			)

						self.assertEqual(vocab_keys[0]		,'''[PAD]'''			)
						self.assertEqual(vocab_keys[1]		,'''[CLS]'''			)
						self.assertEqual(vocab_keys[-1]		,'''j'''			)
						self.assertEqual(len(__lowerCamelCase			)		,10_12			)



		def 		lowerCAmelCase__				(self			)					->      Union[str, Any]:

						"""simple docstring"""






						self.assertEqual(self.get_tokenizer().vocab_size		,10_12			)



		def 		lowerCAmelCase__				(self			)					->      Tuple:

						"""simple docstring"""






						lowerCAmelCase__					:    Dict												=					XLMProphetNetTokenizer(__lowerCamelCase		,keep_accents=__lowerCamelCase			)

						lowerCAmelCase__					:    Tuple												=					tokenizer.tokenize('''This is a test'''			)
						self.assertListEqual(__lowerCamelCase		,['''▁This''', '''▁is''', '''▁a''', '''▁t''', '''est''']			)

						self.assertListEqual(
						    tokenizer.convert_tokens_to_ids(__lowerCamelCase			)		,[value + tokenizer.fairseq_offset for value in [2_85, 46, 10, 1_70, 3_82]]		,)

						lowerCAmelCase__					:    Dict												=					tokenizer.tokenize('''I was born in 92000, and this is falsé.'''			)
						self.assertListEqual(
						    __lowerCamelCase		,[
						        SPIECE_UNDERLINE + '''I''',
						        SPIECE_UNDERLINE + '''was''',
						        SPIECE_UNDERLINE + '''b''',
						        '''or''',
						        '''n''',
						        SPIECE_UNDERLINE + '''in''',
						        SPIECE_UNDERLINE + '''''',
						        '''9''',
						        '''2''',
						        '''0''',
						        '''0''',
						        '''0''',
						        ''',''',
						        SPIECE_UNDERLINE + '''and''',
						        SPIECE_UNDERLINE + '''this''',
						        SPIECE_UNDERLINE + '''is''',
						        SPIECE_UNDERLINE + '''f''',
						        '''al''',
						        '''s''',
						        '''é''',
						        '''.''',
						    ]		,)
						lowerCAmelCase__					:    Optional[Any]												=					tokenizer.convert_tokens_to_ids(__lowerCamelCase			)
						self.assertListEqual(
						    __lowerCamelCase		,[
						        value + tokenizer.fairseq_offset
						        for value in [8, 21, 84, 55, 24, 19, 7, -9, 6_02, 3_47, 3_47, 3_47, 3, 12, 66, 46, 72, 80, 6, -9, 4]
						    ]		,)

						lowerCAmelCase__					:    Optional[Any]												=					tokenizer.convert_ids_to_tokens(__lowerCamelCase			)
						self.assertListEqual(
						    __lowerCamelCase		,[
						        SPIECE_UNDERLINE + '''I''',
						        SPIECE_UNDERLINE + '''was''',
						        SPIECE_UNDERLINE + '''b''',
						        '''or''',
						        '''n''',
						        SPIECE_UNDERLINE + '''in''',
						        SPIECE_UNDERLINE + '''''',
						        '''[UNK]''',
						        '''2''',
						        '''0''',
						        '''0''',
						        '''0''',
						        ''',''',
						        SPIECE_UNDERLINE + '''and''',
						        SPIECE_UNDERLINE + '''this''',
						        SPIECE_UNDERLINE + '''is''',
						        SPIECE_UNDERLINE + '''f''',
						        '''al''',
						        '''s''',
						        '''[UNK]''',
						        '''.''',
						    ]		,)



		@cached_property
		def 		lowerCAmelCase__				(self			)					->      List[str]:

						"""simple docstring"""






						return XLMProphetNetTokenizer.from_pretrained('''microsoft/xprophetnet-large-wiki100-cased'''			)



		@slow
		def 		lowerCAmelCase__				(self			)					->      Tuple:

						"""simple docstring"""






						lowerCAmelCase__					:    Optional[int]												=					'''Hello World!'''
						lowerCAmelCase__					:    str												=					[3_53_89, 66_72, 49, 2]
						self.assertListEqual(__lowerCamelCase		,self.big_tokenizer.encode(__lowerCamelCase			)			)



		@slow
		def 		lowerCAmelCase__				(self			)					->      List[str]:

						"""simple docstring"""






						lowerCAmelCase__					:    Any												=					{'''input_ids''': [[1_10_73, 8_27_83, 18, 26, 8_27_83, 5_49, 5_15_40, 2_48, 1_72_09, 13_01, 2_17, 20, 21_51_86, 13_25, 1_47, 1_72_09, 13_01, 2_17, 20, 5_63_70, 53, 12_20_20, 20, 1_64_77, 27, 8_73_55, 45_48, 20, 47_28, 7_83_92, 17, 15_99_69, 18, 26, 2_44_91, 6_29, 15, 5_38, 2_27_04, 54_39, 15, 27_88, 2_44_91, 98_85, 15, 4_35_34, 6_05, 15, 8_14, 1_84_03, 3_32_00, 29, 15, 4_35_34, 2_44_58, 1_24_10, 1_11, 2_49_66, 8_36_69, 96_37, 14_40_68, 26, 8_50, 2_23_46, 27, 1_47, 2_49_66, 8_36_69, 8_34_90, 26, 3_91_13, 7_35, 27, 6_89, 6_56, 28_00, 13_39, 46_00, 53, 12_20_20, 11_57_85, 34, 8_16, 13_39, 4_68_87, 18, 1_47, 5_39_05, 19_51, 4_22_38, 4_11_70, 1_77_32, 8_34, 4_36, 15, 2_75_23, 9_87_33, 2_17, 1_47, 55_42, 49_81, 9_30, 1_73_47, 16, 2], [2_00_91, 6_29, 94, 8_27_86, 58, 4_90, 20, 15_28, 84, 5_39_05, 3_44, 8_05_92, 11_01_28, 1_88_22, 52_67, 13_06, 62, 15_25_37, 3_08, 79_97, 4_01, 12_44_27, 5_49, 3_54_42, 2_25, 1_09, 1_50_55, 2_57_48, 1_47, 71_19, 4_37_12, 34, 7_67, 13_53_66, 18, 16, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5_92, 6_37_84, 11_94_66, 17, 14_78_08, 8_82_14, 18, 6_56, 81, 32, 32_96, 1_02_80, 16, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], '''attention_mask''': [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}  # noqa: E501
						# fmt: on

						self.tokenizer_integration_test_util(
						    expected_encoding=__lowerCamelCase		,model_name='''microsoft/xprophetnet-large-wiki100-cased'''		,revision='''1acad1643ddd54a44df6a1b797ada8373685d90e'''		,)

