





from ...utils import is_torch_available, is_transformers_available


if is_transformers_available() and is_torch_available():
		from .pipeline_vq_diffusion import LearnedClassifierFreeSamplingEmbeddings, VQDiffusionPipeline








"""simple docstring"""





from __future__ import annotations

from functools import lru_cache
from math import ceil

_a								=						100

_a								=						set(range(3, NUM_PRIMES, 2))
primes.add(2)
_a								=						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=1_00      )
def  lowerCamelCase__						(     __snake_case      )				->						set[int]:


					"""simple docstring"""





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

					_UpperCamelCase									=    set()
					_UpperCamelCase									=    42
					_UpperCamelCase									=    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__						(     __snake_case = 50_00      )				->						int | None:


					"""simple docstring"""





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


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






