


'''simple docstring'''



import math


def 				lowerCamelCase__				(	A       :      int					):




      '''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 				lowerCamelCase__				(	A       :      int = 99_99_66_66_33_33					):




      '''simple docstring'''






      UpperCAmelCase					    =     math.floor(math.sqrt(_UpperCAmelCase					)					) + 1_00
      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())









'''simple docstring'''



from .data_collator import (
    DataCollatorForLanguageModeling,
    DataCollatorForPermutationLanguageModeling,
    DataCollatorForSeqaSeq,
    DataCollatorForSOP,
    DataCollatorForTokenClassification,
    DataCollatorForWholeWordMask,
    DataCollatorWithPadding,
    DefaultDataCollator,
    default_data_collator,
)
from .metrics import glue_compute_metrics, xnli_compute_metrics
from .processors import (
    DataProcessor,
    InputExample,
    InputFeatures,
    SingleSentenceClassificationProcessor,
    SquadExample,
    SquadFeatures,
    SquadVaProcessor,
    SquadVaProcessor,
    glue_convert_examples_to_features,
    glue_output_modes,
    glue_processors,
    glue_tasks_num_labels,
    squad_convert_examples_to_features,
    xnli_output_modes,
    xnli_processors,
    xnli_tasks_num_labels,
)





