from __future__ import annotations

from functools import lru_cache
from math import ceil

_lowerCAmelCase 				=     100

_lowerCAmelCase 				=     set(range(3, NUM_PRIMES, 2))
primes.add(2)
_lowerCAmelCase 				=     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_0_0     )
def     _lowerCAmelCase		(  _lowerCAmelCase     ):
   '''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     _lowerCAmelCase		(  _lowerCAmelCase = 5_0_0_0     ):
   '''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() = }''')













from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_lowerCAmelCase 				=     {
    """configuration_nllb_moe""": [
        """NLLB_MOE_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """NllbMoeConfig""",
    ]
}

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      _lowerCAmelCase 				=     [
          """NLLB_MOE_PRETRAINED_MODEL_ARCHIVE_LIST""",
          """NllbMoeForConditionalGeneration""",
          """NllbMoeModel""",
          """NllbMoePreTrainedModel""",
          """NllbMoeTop2Router""",
          """NllbMoeSparseMLP""",
      ]


if TYPE_CHECKING:
      from .configuration_nllb_moe import (
          NLLB_MOE_PRETRAINED_CONFIG_ARCHIVE_MAP,
          NllbMoeConfig,
      )

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_nllb_moe import (
                NLLB_MOE_PRETRAINED_MODEL_ARCHIVE_LIST,
                NllbMoeForConditionalGeneration,
                NllbMoeModel,
                NllbMoePreTrainedModel,
                NllbMoeSparseMLP,
                NllbMoeTopaRouter,
            )


else:
      import sys

      _lowerCAmelCase 				=     _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)






