"""simple docstring"""






from __future__ import annotations

from functools import lru_cache
from math import ceil

__lowerCAmelCase    :       List[Any]					     =1_0_0

__lowerCAmelCase    :       Tuple					     =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_0_0		)
def 			UpperCAmelCase__       (				lowerCAmelCase__     :int		) ->    set[int]:
      '''simple docstring'''


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

      lowercase														=	set()
      lowercase														=	42
      lowercase														=	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 			UpperCAmelCase__       (				lowerCAmelCase__     :int = 5_0_0_0		) ->    int | None:
      '''simple docstring'''


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


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




"""simple docstring"""






from __future__ import annotations


def 			UpperCAmelCase__       (				lowerCAmelCase__     :list[int]		) ->    int:
      '''simple docstring'''


      if not nums:
            return 0
      lowercase														=	nums[0]
      lowercase														=	0
      for num in nums[1:]:
            lowercase							,							lowercase														=	(
                max_excluding + num,
                max(lowerCAmelCase__					,		lowerCAmelCase__		),
            )
      return max(lowerCAmelCase__					,		lowerCAmelCase__		)


if __name__ == "__main__":
       import doctest

       doctest.testmod()



