

"""simple docstring"""






import math





def 	lowercase      (   __UpperCamelCase						) ->      bool:

 if 1 < number < 4:
  # 2 and 3 are primes
  return True
 elif number < 2 or number % 2 == 0 or number % 3 == 0:
  # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
  return False

 # All primes number are in format of 6k +/- 1
 for i in range(5      ,   int(math.sqrt(__UpperCamelCase						) + 1						)      ,   6						):
  if number % i == 0 or number % (i + 2) == 0:
   return False
 return True





def 	lowercase      (   __UpperCamelCase = 0.1						) ->      int:
 __magic_name__     =      3
 __magic_name__     =      3

 while primes / (2 * j - 1) >= ratio:
  for i in range(j * j + j + 1      ,   (j + 2) * (j + 2)      ,   j + 1						):
   primes += is_prime(__UpperCamelCase						)
  j += 2
 return j


if __name__ == "__main__":
    import doctest

    doctest.testmod()




"""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        _lowercase					(     unittest.TestCase     ):







     @slow
     def 	lowerCAmelCase__    (      self       ):
      __magic_name__     =      AutoModelForSeqaSeqLM.from_pretrained('''google/mt5-small''' ,						return_dict=UpperCamelCase_       ).to(UpperCamelCase_       )
      __magic_name__     =      AutoTokenizer.from_pretrained('''google/mt5-small'''       )

      __magic_name__     =      tokenizer('''Hello there''' ,						return_tensors='''pt'''       ).input_ids
      __magic_name__     =      tokenizer('''Hi I am''' ,						return_tensors='''pt'''       ).input_ids

      __magic_name__     =      model(input_ids.to(UpperCamelCase_       ) ,						labels=labels.to(UpperCamelCase_       )       ).loss
      __magic_name__     =      -(labels.shape[-1] * loss.item())

      __magic_name__     =      -8_4.9_1_2_7
      self.assertTrue(abs(mtf_score - EXPECTED_SCORE       ) < 1E-4       )

