





import math




def 	lowerCAmelCase_					(						__UpperCAmelCase:    int   )   ->			Dict:
    UpperCamelCase__							:       List[str]      =   [True] * n
    UpperCamelCase__							:       Dict      =   False
    UpperCamelCase__							:       Any      =   False
    UpperCamelCase__							:       int      =   True

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

    UpperCamelCase__							:       int      =   [2]

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

    return primes




def 	lowerCAmelCase_					(						__UpperCAmelCase:    int = 9999_6666_3333   )   ->			Tuple:
    UpperCamelCase__							:       Union[str, Any]      =   math.floor(math.sqrt(_lowerCAmelCase   )   ) + 100
    UpperCamelCase__							:       Union[str, Any]      =   prime_sieve(_lowerCAmelCase   )

    UpperCamelCase__							:       List[str]      =   0
    UpperCamelCase__							:       List[Any]      =   0
    UpperCamelCase__							:       Any      =   primes[prime_index]

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

        UpperCamelCase__							:       int      =   last_prime**2
        UpperCamelCase__							:       Optional[int]      =   next_prime**2

        # Get numbers divisible by lps(current)
        UpperCamelCase__							:       int      =   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__							:       Optional[int]      =   upper_bound - next_prime
        while current > lower_bound:
            matches_sum += current
            current -= next_prime

        # Remove the numbers divisible by both ups and lps
        UpperCamelCase__							:       List[Any]      =   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__							:       Optional[Any]      =   next_prime
        prime_index += 1

    return matches_sum


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








import logging
from dataclasses import dataclass, field
from pathlib import Path
from typing import Optional, Union

from .generation.configuration_utils import GenerationConfig
from .training_args import TrainingArguments
from .utils import add_start_docstrings


UpperCAmelCase_  							=				logging.getLogger(__name__)






@dataclass
@add_start_docstrings(TrainingArguments.__doc__       )
class 					lowercase__ (			__lowerCamelCase       ):

   '''simple docstring'''


   a		:							bool     	=	field(default=__lowerCamelCase    ,       metadata={"help": "Whether to use SortishSampler or not."}       )
   a		:							bool     	=	field(
       default=__lowerCamelCase    ,       metadata={"help": "Whether to use generate to calculate generative metrics (ROUGE, BLEU)."}       )
   a		:							Optional[int]     	=	field(
       default=__lowerCamelCase    ,       metadata={
           "help": (
               "The `max_length` to use on each evaluation loop when `predict_with_generate=True`. Will default "
               "to the `max_length` value of the model configuration."
           )
       }    ,       )
   a		:							Optional[int]     	=	field(
       default=__lowerCamelCase    ,       metadata={
           "help": (
               "The `num_beams` to use on each evaluation loop when `predict_with_generate=True`. Will default "
               "to the `num_beams` value of the model configuration."
           )
       }    ,       )
   a		:							Optional[Union[str, Path, GenerationConfig]]     	=	field(
       default=__lowerCamelCase    ,       metadata={
           "help": "Model id, file path or url pointing to a GenerationConfig json file, to use during prediction."
       }    ,       )




   def    UpperCamelCase__						(					self							)				->   str:






       """simple docstring"""
       UpperCamelCase__							:       Tuple      =   super().to_dict()
       for k, v in d.items():
           if isinstance(__magic_name__,	__magic_name__							):
               UpperCamelCase__							:       Tuple      =   v.to_dict()
       return d

