




from __future__ import annotations

from functools import lru_cache
from math import ceil

lowerCamelCase__					:  Any      							=				100

lowerCamelCase__					:  Optional[Any]      							=				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    UpperCAmelCase_				( __UpperCAmelCase		:      int				)   ->					set[int]:
      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    UpperCAmelCase_				( __UpperCAmelCase		:      int = 50_00				)   ->					int | None:
      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'''





class __A     :



 '''simple docstring'''







 def __init__(self					,  A			)       ->	None:


      """simple docstring"""



      _a           =    len(A			)
      _a           =    [0] * len_array

      if len_array > 0:
           _a           =    array[0]

      for i in range(1					,  A			):
           _a           =    self.prefix_sum[i - 1] + array[i]



 def    a__    (self					,  A					,  A			)       ->	int:


      """simple docstring"""



      if start == 0:
           return self.prefix_sum[end]

      return self.prefix_sum[end] - self.prefix_sum[start - 1]



 def    a__    (self					,  A			)       ->	bool:


      """simple docstring"""



      _a           =    {0}
      for sum_item in self.prefix_sum:
           if sum_item - target_sum in sums:
                return True

           sums.add(A			)

      return False


if __name__ == "__main__":
  import doctest

  doctest.testmod()



