




from __future__ import annotations

from functools import lru_cache
from math import ceil

a__      :				Dict   	=			1_00

a__      :				str   	=			set(range(3, NUM_PRIMES, 2))
primes.add(2)
a__      :				str   	=			42

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   _lowerCAmelCase   (						A__	):





      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   _lowerCAmelCase   (						A__ = 5_000	):





      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() = }''')





from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors

def   _lowerCAmelCase   (						A__	):
      lowercase__     =  prime_factors(A__	)
      if is_square_free(A__	):
            return -1 if len(A__	) % 2 else 1
      return 0


if __name__ == "__main__":
       import doctest

       doctest.testmod()
