





import unittest

from transformers import is_flax_available
from transformers.testing_utils import require_flax, require_sentencepiece, require_tokenizers, require_torch, slow


if is_flax_available():
    import optax
    from flax.training.common_utils import onehot

    from transformers import AutoTokenizer, FlaxMTaForConditionalGeneration
    from transformers.models.ta.modeling_flax_ta import shift_tokens_right



@require_torch
@require_sentencepiece
@require_tokenizers
@require_flax
class  A__       (	unittest.TestCase      ):





      @slow
      def 	__UpperCamelCase(			self       ):
       '''simple docstring'''




       UpperCamelCase     : Dict	     =       FlaxMTaForConditionalGeneration.from_pretrained("google/mt5-small"       )
       UpperCamelCase     : Dict	     =       AutoTokenizer.from_pretrained("google/mt5-small"       )

       UpperCamelCase     : Optional[Any]	     =       tokenizer("Hello there"	,							return_tensors="np"       ).input_ids
       UpperCamelCase     : int	     =       tokenizer("Hi I am"	,							return_tensors="np"       ).input_ids

       UpperCamelCase     : Optional[Any]	     =       shift_tokens_right(A_	,							model.config.pad_token_id	,							model.config.decoder_start_token_id       )

       UpperCamelCase     : Union[str, Any]	     =       model(A_	,							decoder_input_ids=A_       ).logits
       UpperCamelCase     : Union[str, Any]	     =       optax.softmax_cross_entropy(A_	,							onehot(A_	,							logits.shape[-1]       )       ).mean()

       UpperCamelCase     : Any	     =       -(labels.shape[-1] * loss.item())

       UpperCamelCase     : int	     =       -84.91_27
       self.assertTrue(abs(mtf_score - EXPECTED_SCORE       ) < 1e-4       )







import math



def 		A_    (					_lowerCAmelCase					)						->			list:
 UpperCamelCase     : str	     =       [True] * n
 UpperCamelCase     : Optional[int]	     =       False
 UpperCamelCase     : str	     =       False
 UpperCamelCase     : List[Any]	     =       True

 for i in range(3							,       int(n**0.5 + 1					)							,       2					):
  UpperCamelCase     : int	     =       i * 2
  while index < n:
   UpperCamelCase     : Optional[Any]	     =       False
   UpperCamelCase     : Optional[Any]	     =       index + i

 UpperCamelCase     : Optional[Any]	     =       [2]

 for i in range(3							,       _lowerCAmelCase							,       2					):
  if is_prime[i]:
   primes.append(_lowerCAmelCase					)

 return primes



def 		A_    (					_lowerCAmelCase = 9999_6666_3333					)						->			int:
 UpperCamelCase     : Tuple	     =       math.floor(math.sqrt(_lowerCAmelCase					)					) + 100
 UpperCamelCase     : Dict	     =       prime_sieve(_lowerCAmelCase					)

 UpperCamelCase     : Optional[Any]	     =       0
 UpperCamelCase     : Tuple	     =       0
 UpperCamelCase     : List[str]	     =       primes[prime_index]

 while (last_prime**2) <= limit:
  UpperCamelCase     : Dict	     =       primes[prime_index + 1]

  UpperCamelCase     : Any	     =       last_prime**2
  UpperCamelCase     : Union[str, Any]	     =       next_prime**2

  # Get numbers divisible by lps(current)
  UpperCamelCase     : Dict	     =       lower_bound + last_prime
  while upper_bound > current <= limit:
   matches_sum += current
   current += last_prime

  # Reset the upper_bound
  while (upper_bound - next_prime) > limit:
   upper_bound -= next_prime

  # Add the numbers divisible by ups(current)
  UpperCamelCase     : List[str]	     =       upper_bound - next_prime
  while current > lower_bound:
   matches_sum += current
   current -= next_prime

  # Remove the numbers divisible by both ups and lps
  UpperCamelCase     : Dict	     =       0
  while upper_bound > current <= limit:
   if current <= lower_bound:
    # Increment the current number
    current += last_prime * next_prime
    continue

   if current > limit:
    break

   # Remove twice since it was added by both ups and lps
   matches_sum -= current * 2

   # Increment the current number
   current += last_prime * next_prime

  # Setup for next pair
  UpperCamelCase     : str	     =       next_prime
  prime_index += 1

 return matches_sum


if __name__ == "__main__":
    print(solution())
