
def 					lowerCamelCase__					(    a__	:	int  )		->						int:
       return n * (2 * n - 1)




def 					lowerCamelCase__					(    a__	:	int  )		->						bool:
       UpperCamelCase_											=							(1 + 24 * n) ** 0.5
       return ((1 + root) / 6) % 1 == 0




def 					lowerCamelCase__					(    a__	:	int = 144  )		->						int:
       UpperCamelCase_											=							start
       UpperCamelCase_											=							hexagonal_num(a__  )
       while not is_pentagonal(a__  ):
              n += 1
              UpperCamelCase_											=							hexagonal_num(a__  )
       return num


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





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_A							=       {'''configuration_dinat''': ['''DINAT_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''DinatConfig''']}


try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      _A							=       [
          '''DINAT_PRETRAINED_MODEL_ARCHIVE_LIST''',
          '''DinatForImageClassification''',
          '''DinatModel''',
          '''DinatPreTrainedModel''',
          '''DinatBackbone''',
      ]

if TYPE_CHECKING:
      from .configuration_dinat import DINAT_PRETRAINED_CONFIG_ARCHIVE_MAP, DinatConfig

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_dinat import (
                DINAT_PRETRAINED_MODEL_ARCHIVE_LIST,
                DinatBackbone,
                DinatForImageClassification,
                DinatModel,
                DinatPreTrainedModel,
            )

else:
      import sys

      _A							=       _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)



