



import math






def 					__lowerCAmelCase		(  __lowerCamelCase	:    int	)  ->						list:
     __lowerCAmelCase	   =[True] * n
     __lowerCAmelCase	   =False
     __lowerCAmelCase	   =False
     __lowerCAmelCase	   =True

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

     __lowerCAmelCase	   =[2]

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

     return primes






def 					__lowerCAmelCase		(  __lowerCamelCase	:    int = 999966663333	)  ->						int:
     __lowerCAmelCase	   =math.floor(math.sqrt(__lowerCamelCase	)	) + 100
     __lowerCAmelCase	   =prime_sieve(__lowerCamelCase	)

     __lowerCAmelCase	   =0
     __lowerCAmelCase	   =0
     __lowerCAmelCase	   =primes[prime_index]

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

          __lowerCAmelCase	   =last_prime**2
          __lowerCAmelCase	   =next_prime**2

          # Get numbers divisible by lps(current)
          __lowerCAmelCase	   =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)
          __lowerCAmelCase	   =upper_bound - next_prime
          while current > lower_bound:
               matches_sum += current
               current -= next_prime

          # Remove the numbers divisible by both ups and lps
          __lowerCAmelCase	   =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
          __lowerCAmelCase	   =next_prime
          prime_index += 1

     return matches_sum


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









from ...configuration_utils import PretrainedConfig
from ...utils import logging


lowercase_	       =			logging.get_logger(__name__)

lowercase_	       =			{
    '''google/realm-cc-news-pretrained-embedder''': (
        '''https://huggingface.co/google/realm-cc-news-pretrained-embedder/resolve/main/config.json'''
    ),
    '''google/realm-cc-news-pretrained-encoder''': (
        '''https://huggingface.co/google/realm-cc-news-pretrained-encoder/resolve/main/config.json'''
    ),
    '''google/realm-cc-news-pretrained-scorer''': (
        '''https://huggingface.co/google/realm-cc-news-pretrained-scorer/resolve/main/config.json'''
    ),
    '''google/realm-cc-news-pretrained-openqa''': (
        '''https://huggingface.co/google/realm-cc-news-pretrained-openqa/aresolve/main/config.json'''
    ),
    '''google/realm-orqa-nq-openqa''': '''https://huggingface.co/google/realm-orqa-nq-openqa/resolve/main/config.json''',
    '''google/realm-orqa-nq-reader''': '''https://huggingface.co/google/realm-orqa-nq-reader/resolve/main/config.json''',
    '''google/realm-orqa-wq-openqa''': '''https://huggingface.co/google/realm-orqa-wq-openqa/resolve/main/config.json''',
    '''google/realm-orqa-wq-reader''': '''https://huggingface.co/google/realm-orqa-wq-reader/resolve/main/config.json''',
    # See all REALM models at https://huggingface.co/models?filter=realm
}






class 						__a (     SCREAMING_SNAKE_CASE				):
	SCREAMING_SNAKE_CASE       =       "realm"



	def __init__(						self							:    Tuple				,	snake_case_							:    Tuple=3_05_22				,	snake_case_							:    List[Any]=7_68				,	snake_case_							:    Any=1_28				,	snake_case_							:    Union[str, Any]=12				,	snake_case_							:    List[str]=12				,	snake_case_							:    Any=8				,	snake_case_							:    Any=30_72				,	snake_case_							:    int="gelu_new"				,	snake_case_							:    Optional[int]=0.1				,	snake_case_							:    Tuple=0.1				,	snake_case_							:    List[Any]=5_12				,	snake_case_							:    List[Any]=2				,	snake_case_							:    Any=0.0_2				,	snake_case_							:    List[str]=1e-12				,	snake_case_							:    Optional[Any]=2_56				,	snake_case_							:    Dict=10				,	snake_case_							:    str=1e-3				,	snake_case_							:    List[str]=5				,	snake_case_							:    Optional[Any]=3_20				,	snake_case_							:    Optional[Any]=13_35_37_18				,	snake_case_							:    Tuple=50_00				,	snake_case_							:    Union[str, Any]=1				,	snake_case_							:    Union[str, Any]=0				,	snake_case_							:    List[str]=2				,	**snake_case_							:    List[str]				,	)->							str:
						super().__init__(pad_token_id=snake_case_				,	bos_token_id=snake_case_				,	eos_token_id=snake_case_				,	**snake_case_)

						# Common config
						__lowerCAmelCase	   =vocab_size
						__lowerCAmelCase	   =max_position_embeddings
						__lowerCAmelCase	   =hidden_size
						__lowerCAmelCase	   =retriever_proj_size
						__lowerCAmelCase	   =num_hidden_layers
						__lowerCAmelCase	   =num_attention_heads
						__lowerCAmelCase	   =num_candidates
						__lowerCAmelCase	   =intermediate_size
						__lowerCAmelCase	   =hidden_act
						__lowerCAmelCase	   =hidden_dropout_prob
						__lowerCAmelCase	   =attention_probs_dropout_prob
						__lowerCAmelCase	   =initializer_range
						__lowerCAmelCase	   =type_vocab_size
						__lowerCAmelCase	   =layer_norm_eps

						# Reader config
						__lowerCAmelCase	   =span_hidden_size
						__lowerCAmelCase	   =max_span_width
						__lowerCAmelCase	   =reader_layer_norm_eps
						__lowerCAmelCase	   =reader_beam_size
						__lowerCAmelCase	   =reader_seq_len

						# Retrieval config
						__lowerCAmelCase	   =num_block_records
						__lowerCAmelCase	   =searcher_beam_size




