

lowerCAmelCase_			      =      range(2, 20 + 1)
lowerCAmelCase_			      =      [10**k for k in range(ks[-1] + 1)]
lowerCAmelCase_			      =      {}


def     __SCREAMING_SNAKE_CASE   (SCREAMING_SNAKE_CASE__    ,						SCREAMING_SNAKE_CASE__    ,						SCREAMING_SNAKE_CASE__    ,						SCREAMING_SNAKE_CASE__			):
						snake_case_  =      sum(a_i[j] for j in range(SCREAMING_SNAKE_CASE__    ,						len(SCREAMING_SNAKE_CASE__			)			)			)
						snake_case_  =      sum(a_i[j] * base[j] for j in range(min(len(SCREAMING_SNAKE_CASE__			)    ,						SCREAMING_SNAKE_CASE__			)			)			)

						snake_case_,       snake_case_  =      0, 0
						snake_case_  =      n - i

						snake_case_  =      memo.get(SCREAMING_SNAKE_CASE__			)

						if sub_memo is not None:
												snake_case_  =      sub_memo.get(SCREAMING_SNAKE_CASE__			)

												if jumps is not None and len(SCREAMING_SNAKE_CASE__			) > 0:
																		# find and make the largest jump without going over
																		snake_case_  =      -1
																		for _k in range(len(SCREAMING_SNAKE_CASE__			) - 1    ,						-1    ,						-1			):
																								if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
																														snake_case_  =      _k
																														break

																		if max_jump >= 0:
																								snake_case_,       snake_case_,       snake_case_  =      jumps[max_jump]
																								# since the difference between jumps is cached, add c
																								snake_case_  =      diff + c
																								for j in range(min(SCREAMING_SNAKE_CASE__    ,						len(SCREAMING_SNAKE_CASE__			)			)			):
																														snake_case_,       snake_case_  =      divmod(SCREAMING_SNAKE_CASE__    ,						10			)
																								if new_c > 0:
																														add(SCREAMING_SNAKE_CASE__    ,						SCREAMING_SNAKE_CASE__    ,						SCREAMING_SNAKE_CASE__			)

												else:
																		snake_case_  =      []
						else:
												snake_case_  =      {c: []}
												snake_case_  =      sub_memo

						if dn >= max_dn or c + diff >= base[k]:
												return diff, dn

						if k > ks[0]:
												while True:
																		# keep doing smaller jumps
																		snake_case_,       snake_case_  =      next_term(SCREAMING_SNAKE_CASE__    ,						k - 1    ,						i + dn    ,						SCREAMING_SNAKE_CASE__			)
																		diff += _diff
																		dn += terms_jumped

																		if dn >= max_dn or c + diff >= base[k]:
																								break
						else:
												# would be too small a jump, just compute sequential terms instead
												snake_case_,       snake_case_  =      compute(SCREAMING_SNAKE_CASE__    ,						SCREAMING_SNAKE_CASE__    ,						i + dn    ,						SCREAMING_SNAKE_CASE__			)
												diff += _diff
												dn += terms_jumped

						snake_case_  =      sub_memo[c]

						# keep jumps sorted by # of terms skipped
						snake_case_  =      0
						while j < len(SCREAMING_SNAKE_CASE__			):
												if jumps[j][1] > dn:
																		break
												j += 1

						# cache the jump for this value digitsum(b) and c
						sub_memo[c].insert(SCREAMING_SNAKE_CASE__    ,						(diff, dn, k)			)
						return (diff, dn)


def     __SCREAMING_SNAKE_CASE   (SCREAMING_SNAKE_CASE__    ,						SCREAMING_SNAKE_CASE__    ,						SCREAMING_SNAKE_CASE__    ,						SCREAMING_SNAKE_CASE__			):
						if i >= n:
												return 0, i
						if k > len(SCREAMING_SNAKE_CASE__			):
												a_i.extend([0 for _ in range(k - len(SCREAMING_SNAKE_CASE__			)			)]			)

						# note: a_i -> b * 10^k + c
						# ds_b -> digitsum(b)
						# ds_c -> digitsum(c)
						snake_case_  =      i
						snake_case_,       snake_case_,       snake_case_  =      0, 0, 0
						for j in range(len(SCREAMING_SNAKE_CASE__			)			):
												if j >= k:
																		ds_b += a_i[j]
												else:
																		ds_c += a_i[j]

						while i < n:
												i += 1
												snake_case_  =      ds_c + ds_b
												diff += addend
												snake_case_  =      0
												for j in range(SCREAMING_SNAKE_CASE__			):
																		snake_case_  =      a_i[j] + addend
																		snake_case_,       snake_case_  =      divmod(SCREAMING_SNAKE_CASE__    ,						10			)

																		ds_c += a_i[j]

												if addend > 0:
																		break

						if addend > 0:
												add(SCREAMING_SNAKE_CASE__    ,						SCREAMING_SNAKE_CASE__    ,						SCREAMING_SNAKE_CASE__			)
						return diff, i - start_i


def     __SCREAMING_SNAKE_CASE   (SCREAMING_SNAKE_CASE__    ,						SCREAMING_SNAKE_CASE__    ,						SCREAMING_SNAKE_CASE__			):
						for j in range(SCREAMING_SNAKE_CASE__    ,						len(SCREAMING_SNAKE_CASE__			)			):
												snake_case_  =      digits[j] + addend
												if s >= 10:
																		snake_case_,       snake_case_  =      divmod(SCREAMING_SNAKE_CASE__    ,						10			)
																		snake_case_  =      addend // 10 + quotient
												else:
																		snake_case_  =      s
																		snake_case_  =      addend // 10

												if addend == 0:
																		break

						while addend > 0:
												snake_case_,       snake_case_  =      divmod(SCREAMING_SNAKE_CASE__    ,						10			)
												digits.append(SCREAMING_SNAKE_CASE__			)


def     __SCREAMING_SNAKE_CASE   (SCREAMING_SNAKE_CASE__ = 10**15			):
						snake_case_  =      [1]
						snake_case_  =      1
						snake_case_  =      0
						while True:
												snake_case_,       snake_case_  =      next_term(SCREAMING_SNAKE_CASE__    ,						20    ,						i + dn    ,						SCREAMING_SNAKE_CASE__			)
												dn += terms_jumped
												if dn == n - i:
																		break

						snake_case_  =      0
						for j in range(len(SCREAMING_SNAKE_CASE__			)			):
												a_n += digits[j] * 10**j
						return a_n


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


a__												=						get_tests_dir('''fixtures/test_sentencepiece.model''')

@require_sentencepiece
class 							UpperCAmelCase_						(     __lowercase							,			unittest.TestCase  ):
							"""simple docstring"""







							UpperCAmelCase__			:		List[str]             =       XLMProphetNetTokenizer
							UpperCAmelCase__			:		Optional[int]             =       False
							UpperCAmelCase__			:		List[Any]             =       True


							def 							__lowercase							(     self			)       ->       int:
												super().setUp()

												# We have a SentencePiece fixture for testing
												_a      :       List[Any]   =						XLMProphetNetTokenizer(_a			,				keep_accents=_a			)
												tokenizer.save_pretrained(self.tmpdirname			)


							def 							__lowercase							(     self			)       ->       Any:
												_a      :       Tuple   =						'''[PAD]'''
												_a      :       int   =						0

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


							def 							__lowercase							(     self			)       ->       str:
												_a      :       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(_a			)			,				1_0_1_2			)


							def 							__lowercase							(     self			)       ->       Union[str, Any]:
												self.assertEqual(self.get_tokenizer().vocab_size			,				1_0_1_2			)


							def 							__lowercase							(     self			)       ->       str:
												_a      :       Tuple   =						XLMProphetNetTokenizer(_a			,				keep_accents=_a			)

												_a      :       Union[str, Any]   =						tokenizer.tokenize('''This is a test'''			)
												self.assertListEqual(_a			,				['''▁This''', '''▁is''', '''▁a''', '''▁t''', '''est''']			)

												self.assertListEqual(
												    tokenizer.convert_tokens_to_ids(_a			)			,				[value + tokenizer.fairseq_offset for value in [2_8_5, 4_6, 1_0, 1_7_0, 3_8_2]]			,				)

												_a      :       Optional[int]   =						tokenizer.tokenize('''I was born in 92000, and this is falsé.'''			)
												self.assertListEqual(
												    _a			,				[
												        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''',
												        '''.''',
												    ]			,				)
												_a      :       List[Any]   =						tokenizer.convert_tokens_to_ids(_a			)
												self.assertListEqual(
												    _a			,				[
												        value + tokenizer.fairseq_offset
												        for value in [8, 2_1, 8_4, 5_5, 2_4, 1_9, 7, -9, 6_0_2, 3_4_7, 3_4_7, 3_4_7, 3, 1_2, 6_6, 4_6, 7_2, 8_0, 6, -9, 4]
												    ]			,				)

												_a      :       List[str]   =						tokenizer.convert_ids_to_tokens(_a			)
												self.assertListEqual(
												    _a			,				[
												        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 							__lowercase							(     self			)       ->       List[str]:
												return XLMProphetNetTokenizer.from_pretrained('''microsoft/xprophetnet-large-wiki100-cased'''			)


							@slow
							def 							__lowercase							(     self			)       ->       Tuple:
												_a      :       str   =						'''Hello World!'''
												_a      :       Tuple   =						[3_5_3_8_9, 6_6_7_2, 4_9, 2]
												self.assertListEqual(_a			,				self.big_tokenizer.encode(_a			)			)




							@slow
							def 							__lowercase							(     self			)       ->       str:
												# fmt: off
												_a      :       str   =						{'''input_ids''': [[1_1_0_7_3, 8_2_7_8_3, 1_8, 2_6, 8_2_7_8_3, 5_4_9, 5_1_5_4_0, 2_4_8, 1_7_2_0_9, 1_3_0_1, 2_1_7, 2_0, 2_1_5_1_8_6, 1_3_2_5, 1_4_7, 1_7_2_0_9, 1_3_0_1, 2_1_7, 2_0, 5_6_3_7_0, 5_3, 1_2_2_0_2_0, 2_0, 1_6_4_7_7, 2_7, 8_7_3_5_5, 4_5_4_8, 2_0, 4_7_2_8, 7_8_3_9_2, 1_7, 1_5_9_9_6_9, 1_8, 2_6, 2_4_4_9_1, 6_2_9, 1_5, 5_3_8, 2_2_7_0_4, 5_4_3_9, 1_5, 2_7_8_8, 2_4_4_9_1, 9_8_8_5, 1_5, 4_3_5_3_4, 6_0_5, 1_5, 8_1_4, 1_8_4_0_3, 3_3_2_0_0, 2_9, 1_5, 4_3_5_3_4, 2_4_4_5_8, 1_2_4_1_0, 1_1_1, 2_4_9_6_6, 8_3_6_6_9, 9_6_3_7, 1_4_4_0_6_8, 2_6, 8_5_0, 2_2_3_4_6, 2_7, 1_4_7, 2_4_9_6_6, 8_3_6_6_9, 8_3_4_9_0, 2_6, 3_9_1_1_3, 7_3_5, 2_7, 6_8_9, 6_5_6, 2_8_0_0, 1_3_3_9, 4_6_0_0, 5_3, 1_2_2_0_2_0, 1_1_5_7_8_5, 3_4, 8_1_6, 1_3_3_9, 4_6_8_8_7, 1_8, 1_4_7, 5_3_9_0_5, 1_9_5_1, 4_2_2_3_8, 4_1_1_7_0, 1_7_7_3_2, 8_3_4, 4_3_6, 1_5, 2_7_5_2_3, 9_8_7_3_3, 2_1_7, 1_4_7, 5_5_4_2, 4_9_8_1, 9_3_0, 1_7_3_4_7, 1_6, 2], [2_0_0_9_1, 6_2_9, 9_4, 8_2_7_8_6, 5_8, 4_9_0, 2_0, 1_5_2_8, 8_4, 5_3_9_0_5, 3_4_4, 8_0_5_9_2, 1_1_0_1_2_8, 1_8_8_2_2, 5_2_6_7, 1_3_0_6, 6_2, 1_5_2_5_3_7, 3_0_8, 7_9_9_7, 4_0_1, 1_2_4_4_2_7, 5_4_9, 3_5_4_4_2, 2_2_5, 1_0_9, 1_5_0_5_5, 2_5_7_4_8, 1_4_7, 7_1_1_9, 4_3_7_1_2, 3_4, 7_6_7, 1_3_5_3_6_6, 1_8, 1_6, 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_9_2, 6_3_7_8_4, 1_1_9_4_6_6, 1_7, 1_4_7_8_0_8, 8_8_2_1_4, 1_8, 6_5_6, 8_1, 3_2, 3_2_9_6, 1_0_2_8_0, 1_6, 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=_a			,				model_name='''microsoft/xprophetnet-large-wiki100-cased'''			,				revision='''1acad1643ddd54a44df6a1b797ada8373685d90e'''			,				)



