




def    UpperCAmelCase__	(  lowerCamelCase ):
  return n * (2 * n - 1)



def    UpperCAmelCase__	(  lowerCamelCase ):
  lowercase     :Optional[Any]   						=    (1 + 24 * n) ** 0.5
  return ((1 + root) / 6) % 1 == 0



def    UpperCAmelCase__	(  lowerCamelCase = 144 ):
  lowercase     :Any   						=    start
  lowercase     :Optional[int]   						=    hexagonal_num(lowerCamelCase )
  while not is_pentagonal(lowerCamelCase ):
    n += 1
    lowercase     :List[str]   						=    hexagonal_num(lowerCamelCase )
  return num


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









from unittest.mock import patch

import datasets
from datasets import Dataset



def    UpperCAmelCase__	(  ):
  lowercase     :Any   						=    Dataset.from_dict({"col_1": [3, 2, 0, 1]} )

  with patch("tqdm.auto.tqdm" ) as mock_tqdm:
    datasets.disable_progress_bar()
    dset.map(lambda lowerCamelCase : {"col_2": x["col_1"] + 1} )
    mock_tqdm.assert_not_called()

    mock_tqdm.reset_mock()

    datasets.enable_progress_bar()
    dset.map(lambda lowerCamelCase : {"col_2": x["col_1"] + 1} )
    mock_tqdm.assert_called()



