from __future__ import annotations
def 				__lowercase	(						lowerCamelCase__					)				->list[int]:

  '''simple docstring'''




  a__     		=     [0] * max_one

  for i in range(0 ,				lowerCamelCase__					):
    a__     		=     i

  for i in range(2 ,				lowerCamelCase__					):
    if totients[i] == i:
      for j in range(lowerCamelCase__ ,				lowerCamelCase__ ,				lowerCamelCase__					):
        totients[j] -= totients[j] // i

  return totients
def 				__lowercase	(						lowerCamelCase__ ,				lowerCamelCase__					)				->bool:

  '''simple docstring'''




  return sorted(str(lowerCamelCase__					)					) == sorted(str(lowerCamelCase__					)					)
def 				__lowercase	(						lowerCamelCase__ = 10_00_00_00					)				->int:

  '''simple docstring'''




  a__     		=     1  # i
  a__     		=     0  # φ(i)
  a__     		=     get_totients(max_n + 1					)

  for i in range(2 ,				max_n + 1					):
    a__     		=     totients[i]

    if i * min_denominator < min_numerator * t and has_same_digits(lowerCamelCase__ ,				lowerCamelCase__					):
      a__     		=     i
      a__     		=     t

  return min_numerator


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


from unittest.mock import patch

import datasets
from datasets import Dataset
def 				__lowercase	(						)				->Union[str, Any]:

  '''simple docstring'''




  a__     		=     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()

