

def      a      (			A__	:   int     )    ->      bool:





      """simple docstring"""



      _lowercase	       =(1 + 24 * n) ** 0.5
      return ((1 + root) / 6) % 1 == 0
def      a      (			A__	:   int = 5000     )    ->      int:





      """simple docstring"""



      _lowercase	       =[(i * (3 * i - 1)) // 2 for i in range(1      ,   A__     )]
      for i, pentagonal_i in enumerate(A__     ):
            for j in range(A__      ,   len(A__     )     ):
                  _lowercase	       =pentagonal_nums[j]
                  _lowercase	       =pentagonal_i + pentagonal_j
                  _lowercase	       =pentagonal_j - pentagonal_i
                  if is_pentagonal(A__     ) and is_pentagonal(A__     ):
                        return b

      return -1


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





from .imports import is_tqdm_available


if is_tqdm_available():
  from tqdm.auto import tqdm as _tqdm

from ..state import PartialState
def      a      (			A__	:   bool = True      ,   *A__	:   int      ,   **A__	:   Union[str, Any]     )    ->      List[str]:





      """simple docstring"""



      if not is_tqdm_available():
            raise ImportError('Accelerate\'s `tqdm` module requires `tqdm` to be installed. Please run `pip install tqdm`.'     )
      _lowercase	       =False
      if main_process_only:
            _lowercase	       =PartialState().local_process_index == 0
      return _tqdm(*A__      ,   **A__      ,   disable=A__     )


