



def   __snake_case			(    _UpperCAmelCase = 1000       ):
    __a		 =       -1
    __a		 =       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
        __a		 =       (n * n - 2 * a * n) // (2 * n - 2 * a)
        __a		 =       n - a - b
        if c * c == (a * a + b * b):
            __a		 =       a * b * c
            if candidate >= product:
                __a		 =       candidate
    return product


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










from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_torch_available,
    is_vision_available,
)


__snake_case		:Union[str, Any]   	=  {'''configuration_vit''': ['''VIT_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''ViTConfig''', '''ViTOnnxConfig''']}

try:
 if not is_vision_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __snake_case		:List[str]   	=  ['''ViTFeatureExtractor''']
 __snake_case		:Optional[Any]   	=  ['''ViTImageProcessor''']

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __snake_case		:str   	=  [
     '''VIT_PRETRAINED_MODEL_ARCHIVE_LIST''',
     '''ViTForImageClassification''',
     '''ViTForMaskedImageModeling''',
     '''ViTModel''',
     '''ViTPreTrainedModel''',
 ]

try:
 if not is_tf_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __snake_case		:Tuple   	=  [
     '''TFViTForImageClassification''',
     '''TFViTModel''',
     '''TFViTPreTrainedModel''',
 ]

try:
 if not is_flax_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __snake_case		:Tuple   	=  [
     '''FlaxViTForImageClassification''',
     '''FlaxViTModel''',
     '''FlaxViTPreTrainedModel''',
 ]

if TYPE_CHECKING:
 from .configuration_vit import VIT_PRETRAINED_CONFIG_ARCHIVE_MAP, ViTConfig, ViTOnnxConfig

 try:
  if not is_vision_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .feature_extraction_vit import ViTFeatureExtractor
  from .image_processing_vit import ViTImageProcessor

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_vit import (
      VIT_PRETRAINED_MODEL_ARCHIVE_LIST,
      ViTForImageClassification,
      ViTForMaskedImageModeling,
      ViTModel,
      ViTPreTrainedModel,
  )

 try:
  if not is_tf_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_tf_vit import TFViTForImageClassification, TFViTModel, TFViTPreTrainedModel

 try:
  if not is_flax_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_flax_vit import FlaxViTForImageClassification, FlaxViTModel, FlaxViTPreTrainedModel


else:
 import sys

 __snake_case		:Optional[int]   	=  _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)





