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

from functools import lru_cache
from math import ceil

A__   :		int 		=100

A__   :		Tuple 		=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=100 )
def        A_     (						__SCREAMING_SNAKE_CASE						:  int )				->       set[int]:





  """simple docstring"""

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

  __A		:     set[int]												=		set()
  __A		:     int
  __A		:     int

  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_     (						__SCREAMING_SNAKE_CASE						:  int = 5000 )				->       int | None:





  """simple docstring"""

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


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





'''simple docstring'''
from collections.abc import Sequence







def        A_     (						__SCREAMING_SNAKE_CASE						:  Sequence[float]			,     __SCREAMING_SNAKE_CASE						:  bool = False )				->       float:





  """simple docstring"""

  if not arr:
    return 0

  __A		:     Any												=		0 if allow_empty_subarrays else float("""-inf""" )
  __A		:     List[Any]												=		0.0
  for num in arr:
    __A		:     Tuple												=		max(0 if allow_empty_subarrays else num			,     curr_sum + num )
    __A		:     Optional[int]												=		max(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )

  return max_sum


if __name__ == "__main__":
     from doctest import testmod

     testmod()

     A__   :		Any 		=[-2, 1, -3, 4, -1, 2, 1, -5, 4]
     print(F"{max_subarray_sum(nums) = }")



