



"""simple docstring"""






import math






def 	snake_case_  (				A_ :		int						):


       '''simple docstring'''





       _lowerCamelCase						:    List[Any]         =			[True] * n
       _lowerCamelCase						:    Optional[int]         =			False
       _lowerCamelCase						:    Union[str, Any]         =			False
       _lowerCamelCase						:    Tuple         =			True

       for i in range(3,    int(n**0.5 + 1						),    2						):
              _lowerCamelCase						:    Dict         =			i * 2
              while index < n:
                     _lowerCamelCase						:    List[str]         =			False
                     _lowerCamelCase						:    Union[str, Any]         =			index + i

       _lowerCamelCase						:    Optional[Any]         =			[2]

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

       return primes






def 	snake_case_  (				A_ :		int = 99_99_66_66_33_33						):


       '''simple docstring'''





       _lowerCamelCase						:    List[str]         =			math.floor(math.sqrt(A_						)						) + 1_00
       _lowerCamelCase						:    Any         =			prime_sieve(A_						)

       _lowerCamelCase						:    Dict         =			0
       _lowerCamelCase						:    str         =			0
       _lowerCamelCase						:    Optional[int]         =			primes[prime_index]

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

              _lowerCamelCase						:    Union[str, Any]         =			last_prime**2
              _lowerCamelCase						:    List[str]         =			next_prime**2

              # Get numbers divisible by lps(current)
              _lowerCamelCase						:    List[Any]         =			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						:    List[str]         =			upper_bound - next_prime
              while current > lower_bound:
                     matches_sum += current
                     current -= next_prime

              # Remove the numbers divisible by both ups and lps
              _lowerCamelCase						:    Optional[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
              _lowerCamelCase						:    Dict         =			next_prime
              prime_index += 1

       return matches_sum


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







"""simple docstring"""






import timeit

import numpy as np

import datasets
from datasets.arrow_writer import ArrowWriter
from datasets.features.features import _ArrayXD






def 	snake_case_  (				A_ :		Optional[int]						):


       '''simple docstring'''





       def wrapper(*A_ :		int,    **A_ :		List[str]						):
              _lowerCamelCase						:    Tuple         =			timeit.default_timer()
              _lowerCamelCase						:    Optional[Any]         =			func(*A_,    **A_						)
              _lowerCamelCase						:    Tuple         =			timeit.default_timer() - starttime
              return delta

       _lowerCamelCase						:    Optional[Any]         =			func.__name__

       return wrapper






def 	snake_case_  (				A_ :		dict,    A_ :		List[str]=1_00,    A_ :		Optional[Any]=None						):


       '''simple docstring'''





       _lowerCamelCase						:    Union[str, Any]         =			[]
       _lowerCamelCase						:    Optional[int]         =			seq_shapes or {}
       for i in range(A_						):
              _lowerCamelCase						:    Any         =			{}
              for col_id, (k, v) in enumerate(features.items()						):
                     if isinstance(A_,    _ArrayXD						):
                            _lowerCamelCase						:    str         =			np.random.rand(*v.shape						).astype(v.dtype						)
                     elif isinstance(A_,    datasets.Value						):
                            if v.dtype == "string":
                                   _lowerCamelCase						:    List[str]         =			'''The small grey turtle was surprisingly fast when challenged.'''
                            else:
                                   _lowerCamelCase						:    int         =			np.random.randint(10,    size=1						).astype(v.dtype						).item()
                     elif isinstance(A_,    datasets.Sequence						):
                            while isinstance(A_,    datasets.Sequence						):
                                   _lowerCamelCase						:    Union[str, Any]         =			v.feature
                            _lowerCamelCase						:    Dict         =			seq_shapes[k]
                            _lowerCamelCase						:    int         =			np.random.rand(*A_						).astype(v.dtype						)
                     _lowerCamelCase						:    Optional[Any]         =			data

              dummy_data.append((i, example)						)

       return dummy_data







def 	snake_case_  (				A_ :		List[str],    A_ :		Optional[int],    A_ :		Optional[int]=1_00,    A_ :		Optional[Any]=None						):


       '''simple docstring'''





       _lowerCamelCase						:    Optional[int]         =			generate_examples(A_,    num_examples=A_,    seq_shapes=A_						)

       with ArrowWriter(features=A_,    path=A_						) as writer:
              for key, record in dummy_data:
                     _lowerCamelCase						:    Optional[Any]         =			features.encode_example(A_						)
                     writer.write(A_						)

              _lowerCamelCase      ,   _lowerCamelCase						:    Dict         =			writer.finalize()

       if not num_final_examples == num_examples:
              raise ValueError(
                  F'''Error writing the dataset, wrote {num_final_examples} examples but should have written {num_examples}.'''						)

       _lowerCamelCase						:    List[Any]         =			datasets.Dataset.from_file(filename=A_,    info=datasets.DatasetInfo(features=A_						)						)

       return dataset


