






def       _a   (							lowerCamelCase__				)  ->      Any:
 lowerCamelCase_							:    str							=     [7_01, 3_01, 1_32, 57, 23, 10, 4, 1]
 for gap in gaps:
  for i in range(lowerCamelCase__ ,			len(lowerCamelCase__				)				):
   lowerCamelCase_							:    int							=     collection[i]
   lowerCamelCase_							:    Dict							=     i
   while j >= gap and collection[j - gap] > insert_value:
    lowerCamelCase_							:    Tuple							=     collection[j - gap]
    j -= gap
   if j != i:
    lowerCamelCase_							:    Optional[int]							=     insert_value
 return collection


if __name__ == "__main__":
       from doctest import testmod

       testmod()
       UpperCamelCase											=      input('''Enter numbers separated by a comma:\n''').strip()
       UpperCamelCase											=      [int(item) for item in user_input.split(''',''')]
       print(shell_sort(unsorted))








from __future__ import annotations




def       _a   (							lowerCamelCase__				)  ->      list[int]:
 lowerCamelCase_							:    Any							=     [0] * max_one

 for i in range(0 ,			lowerCamelCase__				):
  lowerCamelCase_							:    Union[str, Any]							=     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       _a   (							lowerCamelCase__ ,			lowerCamelCase__				)  ->      bool:
 return sorted(str(lowerCamelCase__				)				) == sorted(str(lowerCamelCase__				)				)




def       _a   (							lowerCamelCase__ = 10_00_00_00				)  ->      int:
 lowerCamelCase_							:    Tuple							=     1  # i
 lowerCamelCase_							:    Union[str, Any]							=     0  # φ(i)
 lowerCamelCase_							:    List[Any]							=     get_totients(max_n + 1				)

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

  if i * min_denominator < min_numerator * t and has_same_digits(lowerCamelCase__ ,			lowerCamelCase__				):
   lowerCamelCase_							:    str							=     i
   lowerCamelCase_							:    List[Any]							=     t

 return min_numerator


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