




def     lowercase		(  _lowerCAmelCase = 100_0000   ):
  UpperCAmelCase__         = limit + 1
  UpperCAmelCase__         = [0] * limit
  for first_term in range(1 ,  _lowerCAmelCase   ):
    for n in range(_lowerCAmelCase ,  _lowerCAmelCase ,  _lowerCAmelCase   ):
      UpperCAmelCase__         = first_term + n / first_term
      if common_difference % 4:  # d must be divisble by 4
        continue
      else:
        common_difference /= 4
        if (
            first_term > common_difference
            and first_term < 4 * common_difference
        ):  # since x,y,z are positive integers
          frequency[n] += 1  # so z>0 and a>d ,also 4d<a

  UpperCAmelCase__         = sum(1 for x in frequency[1:limit] if x == 10   )

  return count


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       lowerCamelCase	(       unittest.TestCase   ):


  '''simple docstring'''







  @slow
  def  _a      (self	):


        """simple docstring"""

        UpperCAmelCase__			:							Dict							=    AutoModelForSeqaSeqLM.from_pretrained("""google/mt5-small"""							,       return_dict=_lowerCamelCase	).to(_lowerCamelCase	)
        UpperCAmelCase__			:							Optional[Any]							=    AutoTokenizer.from_pretrained("""google/mt5-small"""	)

        UpperCAmelCase__			:							Any							=    tokenizer("""Hello there"""							,       return_tensors="""pt"""	).input_ids
        UpperCAmelCase__			:							str							=    tokenizer("""Hi I am"""							,       return_tensors="""pt"""	).input_ids

        UpperCAmelCase__			:							Tuple							=    model(input_ids.to(_lowerCamelCase	)							,       labels=labels.to(_lowerCamelCase	)	).loss
        UpperCAmelCase__			:							Union[str, Any]							=    -(labels.shape[-1] * loss.item())

        UpperCAmelCase__			:							List[str]							=    -84.9_127
        self.assertTrue(abs(mtf_score - EXPECTED_SCORE	) < 1e-4	)

