import math





def        lowercase(     UpperCamelCase_    )						->     str:







 '''simple docstring'''
 UpperCamelCase          =	[True] * n
 UpperCamelCase          =	False
 UpperCamelCase          =	False
 UpperCamelCase          =	True

 for i in range(3				, int(n**0.5 + 1    )				, 2    ):
  UpperCamelCase          =	i * 2
  while index < n:
   UpperCamelCase          =	False
   UpperCamelCase          =	index + i

 UpperCamelCase          =	[2]

 for i in range(3				, UpperCamelCase_				, 2    ):
  if is_prime[i]:
   primes.append(UpperCamelCase_    )

 return primes





def        lowercase(     UpperCamelCase_ = 999966663333    )						->     Any:







 '''simple docstring'''
 UpperCamelCase          =	math.floor(math.sqrt(UpperCamelCase_    )    ) + 100
 UpperCamelCase          =	prime_sieve(UpperCamelCase_    )

 UpperCamelCase          =	0
 UpperCamelCase          =	0
 UpperCamelCase          =	primes[prime_index]

 while (last_prime**2) <= limit:
  UpperCamelCase          =	primes[prime_index + 1]

  UpperCamelCase          =	last_prime**2
  UpperCamelCase          =	next_prime**2

  # Get numbers divisible by lps(current)
  UpperCamelCase          =	lower_bound + last_prime
  while upper_bound > current <= limit:
   matches_sum += current
   current += last_prime

  # Reset the upper_bound
  while (upper_bound - next_prime) > limit:
   upper_bound -= next_prime

  # Add the numbers divisible by ups(current)
  UpperCamelCase          =	upper_bound - next_prime
  while current > lower_bound:
   matches_sum += current
   current -= next_prime

  # Remove the numbers divisible by both ups and lps
  UpperCamelCase          =	0
  while upper_bound > current <= limit:
   if current <= lower_bound:
    # Increment the current number
    current += last_prime * next_prime
    continue

   if current > limit:
    break

   # Remove twice since it was added by both ups and lps
   matches_sum -= current * 2

   # Increment the current number
   current += last_prime * next_prime

  # Setup for next pair
  UpperCamelCase          =	next_prime
  prime_index += 1

 return matches_sum


if __name__ == "__main__":
     print(solution())

import json
import os
import unittest

from transformers.models.xlm.tokenization_xlm import VOCAB_FILES_NAMES, XLMTokenizer
from transformers.testing_utils import slow

from ...test_tokenization_common import TokenizerTesterMixin





class 		_lowercase						(					snake_case_						,      unittest.TestCase       ):
 lowercase				     =   XLMTokenizer
 lowercase				     =   False

 def 						SCREAMING_SNAKE_CASE__   ( self	:							Any			)   ->						List[Any]:

  """simple docstring"""





  super().setUp()

  # Adapted from Sennrich et al. 2015 and https://github.com/rsennrich/subword-nmt
  UpperCamelCase_					:						List[Any] =					[
      'l',
      'o',
      'w',
      'e',
      'r',
      's',
      't',
      'i',
      'd',
      'n',
      'w</w>',
      'r</w>',
      't</w>',
      'lo',
      'low',
      'er</w>',
      'low</w>',
      'lowest</w>',
      'newer</w>',
      'wider</w>',
      '<unk>',
  ]
  UpperCamelCase_					:						str =					dict(zip(snake_case   ,      range(len(snake_case			)			)			)			)
  UpperCamelCase_					:						Tuple =					['l o 123', 'lo w 1456', 'e r</w> 1789', '']

  UpperCamelCase_					:						Tuple =					os.path.join(self.tmpdirname   ,      VOCAB_FILES_NAMES['vocab_file']			)
  UpperCamelCase_					:						Any =					os.path.join(self.tmpdirname   ,      VOCAB_FILES_NAMES['merges_file']			)
  with open(self.vocab_file   ,      'w'			) as fp:
   fp.write(json.dumps(snake_case			)			)
  with open(self.merges_file   ,      'w'			) as fp:
   fp.write('\n'.join(snake_case			)			)

 def 						SCREAMING_SNAKE_CASE__   ( self	:							List[Any]   ,      snake_case	:							Union[str, Any]			)   ->						int:

  """simple docstring"""





  UpperCamelCase_					:						Tuple =					'lower newer'
  UpperCamelCase_					:						Optional[int] =					'lower newer'
  return input_text, output_text

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

  """simple docstring"""





  UpperCamelCase_					:						int =					XLMTokenizer(self.vocab_file   ,      self.merges_file			)

  UpperCamelCase_					:						List[str] =					'lower'
  UpperCamelCase_					:						Optional[int] =					['low', 'er</w>']
  UpperCamelCase_					:						Optional[Any] =					tokenizer.tokenize(snake_case			)
  self.assertListEqual(snake_case   ,      snake_case			)

  UpperCamelCase_					:						List[Any] =					tokens + ['<unk>']
  UpperCamelCase_					:						int =					[1_4, 1_5, 2_0]
  self.assertListEqual(tokenizer.convert_tokens_to_ids(snake_case			)   ,      snake_case			)


 @slow
 def 						SCREAMING_SNAKE_CASE__   ( self	:							List[Any]			)   ->						Optional[int]:

  """simple docstring"""





  UpperCamelCase_					:						int =					XLMTokenizer.from_pretrained('xlm-mlm-en-2048'			)

  UpperCamelCase_					:						int =					tokenizer.encode('sequence builders'   ,      add_special_tokens=snake_case			)
  UpperCamelCase_					:						Optional[int] =					tokenizer.encode('multi-sequence build'   ,      add_special_tokens=snake_case			)

  UpperCamelCase_					:						Tuple =					tokenizer.build_inputs_with_special_tokens(snake_case			)
  UpperCamelCase_					:						Any =					tokenizer.build_inputs_with_special_tokens(snake_case   ,      snake_case			)

  assert encoded_sentence == [0] + text + [1]
  assert encoded_pair == [0] + text + [1] + text_a + [1]



