

'''simple docstring'''
from __future__ import annotations

from functools import lru_cache
from math import ceil

lowerCamelCase			:				Union[str, Any] 			=					1_0_0

lowerCamelCase			:				Optional[int] 			=					set(range(3, NUM_PRIMES, 2))
primes.add(2)
lowerCamelCase			:				int

for prime in range(3, ceil(NUM_PRIMES**0.5), 2):
     if prime not in primes:
          continue
     primes.difference_update(set(range(prime * prime, NUM_PRIMES, prime)))


@lru_cache(maxsize=1_00    )
def 	_lowerCAmelCase (						_UpperCamelCase						:					int    )				->      set[int]:
     """simple docstring"""




     if number_to_partition < 0:
          return set()
     elif number_to_partition == 0:
          return {1}

     _SCREAMING_SNAKE_CASE							   =set()
     _SCREAMING_SNAKE_CASE							   =42
     _SCREAMING_SNAKE_CASE							   =42

     for prime in primes:
          if prime > number_to_partition:
               continue
          for sub in partition(number_to_partition - prime    ):
               ret.add(sub * prime    )

     return ret


def 	_lowerCAmelCase (						_UpperCamelCase						:					int = 50_00    )				->      int | None:
     """simple docstring"""




     for number_to_partition in range(1							,			_UpperCamelCase    ):
          if len(partition(_UpperCamelCase    )    ) > number_unique_partitions:
               return number_to_partition
     return None


if __name__ == "__main__":
     print(f'''{solution() = }''')



'''simple docstring'''
import warnings


warnings.warn(
    "memory_utils has been reorganized to utils.memory. Import `find_executable_batchsize` from the main `__init__`: "
    "`from accelerate import find_executable_batch_size` to avoid this warning.",
    FutureWarning,
)
