
def 		lowercase_    (     A__ = 1000	)							->							int:
    """simple docstring"""

    snake_case				  =      -1
    snake_case				  =      0
    for a in range(1				,	n // 3	):
        # Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
        snake_case				  =      (n * n - 2 * a * n) // (2 * n - 2 * a)
        snake_case				  =      n - a - b
        if c * c == (a * a + b * b):
            snake_case				  =      a * b * c
            if candidate >= product:
                snake_case				  =      candidate
    return product


if __name__ == "__main__":
   print(f"{solution() = }")



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						):





     @slow
     def 	UpperCAmelCase(self   :					List[str]     )		->		Optional[int]:
         snake_case				  =      AutoModelForSeqaSeqLM.from_pretrained("google/mt5-small"       ,					return_dict=_A     ).to(_A     )
         snake_case				  =      AutoTokenizer.from_pretrained("google/mt5-small"     )

         snake_case				  =      tokenizer("Hello there"       ,					return_tensors="pt"     ).input_ids
         snake_case				  =      tokenizer("Hi I am"       ,					return_tensors="pt"     ).input_ids

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

         snake_case				  =      -84.91_27
         self.assertTrue(abs(mtf_score - EXPECTED_SCORE     ) < 1E-4     )

