

'''simple docstring'''
import pytest

from datasets.parallel import ParallelBackendConfig, parallel_backend
from datasets.utils.py_utils import map_nested

from .utils import require_dill_gt_0_3_2, require_joblibspark, require_not_windows


def        _lowerCAmelCase					(						_UpperCamelCase						:     Optional[int]				)      ->			Optional[int]:  # picklable for multiprocessing
     """simple docstring"""




     return i + 1


@require_dill_gt_0_3_2
@require_joblibspark
@require_not_windows
def        _lowerCAmelCase					(						)      ->			List[Any]:
     """simple docstring"""




     with parallel_backend('spark'				):
          assert ParallelBackendConfig.backend_name == "spark"

     _SCREAMING_SNAKE_CASE							    =[1, 2, 3]
     with pytest.raises(_UpperCamelCase				):
          with parallel_backend('unsupported backend'				):
               map_nested(_UpperCamelCase							, _UpperCamelCase							, num_proc=2				)

     with pytest.raises(_UpperCamelCase				):
          with parallel_backend('unsupported backend'				):
               map_nested(_UpperCamelCase							, _UpperCamelCase							, num_proc=-1				)







@require_dill_gt_0_3_2
@require_joblibspark
@require_not_windows
@pytest.mark.parametrize('num_proc'							, [2, -1]				)
def        _lowerCAmelCase					(						_UpperCamelCase						:     Tuple				)      ->			Tuple:
     """simple docstring"""




     _SCREAMING_SNAKE_CASE							    =[1, 2]
     _SCREAMING_SNAKE_CASE							    ={'a': 1, 'b': 2}
     _SCREAMING_SNAKE_CASE							    ={'a': [1, 2], 'b': [3, 4]}
     _SCREAMING_SNAKE_CASE							    ={'a': {'1': 1}, 'b': 2}
     _SCREAMING_SNAKE_CASE							    ={'a': 1, 'b': 2, 'c': 3, 'd': 4}
     _SCREAMING_SNAKE_CASE							    =[2, 3]
     _SCREAMING_SNAKE_CASE							    ={'a': 2, 'b': 3}
     _SCREAMING_SNAKE_CASE							    ={'a': [2, 3], 'b': [4, 5]}
     _SCREAMING_SNAKE_CASE							    ={'a': {'1': 2}, 'b': 3}
     _SCREAMING_SNAKE_CASE							    ={'a': 2, 'b': 3, 'c': 4, 'd': 5}

     with parallel_backend('spark'				):
          assert map_nested(_UpperCamelCase							, _UpperCamelCase							, num_proc=_UpperCamelCase				) == expected_map_nested_sa
          assert map_nested(_UpperCamelCase							, _UpperCamelCase							, num_proc=_UpperCamelCase				) == expected_map_nested_sa
          assert map_nested(_UpperCamelCase							, _UpperCamelCase							, num_proc=_UpperCamelCase				) == expected_map_nested_sa
          assert map_nested(_UpperCamelCase							, _UpperCamelCase							, num_proc=_UpperCamelCase				) == expected_map_nested_sa
          assert map_nested(_UpperCamelCase							, _UpperCamelCase							, num_proc=_UpperCamelCase				) == expected_map_nested_sa








import math
def 						_a    (      a :int )							->			list:
 a		  =      [True] * n
 a		  =      False
 a		  =      False
 a		  =      True

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

 a		  =      [2]

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

 return primes
def 						_a    (      a :int = 999_966_663_333 )							->			int:
 a		  =      math.floor(math.sqrt(a ) ) + 100
 a		  =      prime_sieve(a )

 a		  =      0
 a		  =      0
 a		  =      primes[prime_index]

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

  a		  =      last_prime**2
  a		  =      next_prime**2

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

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

 return matches_sum


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


