
"""simple docstring"""




from __future__ import annotations

from functools import lru_cache
from math import ceil

_A     :			List[str]  						=			1_00

_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     __magic_name__      ( __snake_case							:			int    )					->							set[int]:
       if number_to_partition < 0:
              return set()
       elif number_to_partition == 0:
              return {1}

       lowercase       :							set[int]									=				set()
       lowercase       :							int
       lowercase       :							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     __magic_name__      ( __snake_case							:			int = 5000    )					->							int | None:
       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() = }")




"""simple docstring"""




import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_sentencepiece, require_tokenizers, require_torch, slow, torch_device


if is_torch_available():
   from transformers import AutoModelForSeqaSeqLM, AutoTokenizer

@require_torch
@require_sentencepiece
@require_tokenizers
class 						a__		( unittest.TestCase		):
   @slow
   def      __magic_name__     (     self							):
          lowercase       :							Tuple									=				AutoModelForSeqaSeqLM.from_pretrained("google/mt5-small"      ,       return_dict=_a							).to(_a							)
          lowercase       :							Union[str, Any]									=				AutoTokenizer.from_pretrained("google/mt5-small"							)

          lowercase       :							Optional[Any]									=				tokenizer("Hello there"      ,       return_tensors="pt"							).input_ids
          lowercase       :							Union[str, Any]									=				tokenizer("Hi I am"      ,       return_tensors="pt"							).input_ids

          lowercase       :							int									=				model(input_ids.to(_a							)      ,       labels=labels.to(_a							)							).loss
          lowercase       :							str									=				-(labels.shape[-1] * loss.item())

          lowercase       :							List[str]									=				-8_4.9_1_2_7
          self.assertTrue(abs(mtf_score - EXPECTED_SCORE							) < 1E-4							)


