


'''simple docstring'''




from __future__ import annotations

from functools import lru_cache
from math import ceil

_a   :   Optional[Any]												=   100

_a   :   Dict												=   set(range(3, NUM_PRIMES, 2))
primes.add(2)
_a   :   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_0_0						)
def   _a		(lowercase__			:   int						)			->			set[int]:






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

     __snake_case           =						set()
     __snake_case           =						42
     __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   _a		(lowercase__			:   int = 5_0_0_0						)			->			int | None:






     """simple docstring"""
     for number_to_partition in range(1							,   lowercase__						):
          if len(partition(lowercase__						)						) > number_unique_partitions:
               return number_to_partition
     return None


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







def 							__SCREAMING_SNAKE_CASE     (   a__    :   int       )					->				int:
	if not isinstance(a__			,a__       ):
		raise TypeError("""Input value must be an 'int' type"""       )

	__A :			Union[str, Any]		    =			0
	while number:
		position += 1
		number >>= 1

	return position


if __name__ == "__main__":
			import doctest

			doctest.testmod()





