



"""simple docstring"""




from math import gcd


def 	lowercase__  (      _UpperCAmelCase = 1_20_00					)  ->      int:






      '''simple docstring'''


      lowercase	:   int											= 0
      for d in range(max_d + 1					):
            for n in range(d // 3 + 1						,   (d + 1) // 2					):
                  if gcd(_UpperCAmelCase						,   _UpperCAmelCase					) == 1:
                        fractions_number += 1
      return fractions_number


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





"""simple docstring"""




from __future__ import annotations


def 	lowercase__  (      _UpperCAmelCase					)  ->      list[int]:






      '''simple docstring'''


      lowercase	:   Optional[Any]											= [0] * max_one

      for i in range(0						,   _UpperCAmelCase					):
            lowercase	:   List[Any]											= i

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

      return totients


def 	lowercase__  (      _UpperCAmelCase						,   _UpperCAmelCase					)  ->      bool:






      '''simple docstring'''


      return sorted(str(_UpperCAmelCase					)					) == sorted(str(_UpperCAmelCase					)					)


def 	lowercase__  (      _UpperCAmelCase = 10_00_00_00					)  ->      int:






      '''simple docstring'''


      lowercase	:   Union[str, Any]											= 1  # i
      lowercase	:   Any											= 0  # φ(i)
      lowercase	:   int											= get_totients(max_n + 1					)

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

            if i * min_denominator < min_numerator * t and has_same_digits(_UpperCAmelCase						,   _UpperCAmelCase					):
                  lowercase	:   List[Any]											= i
                  lowercase	:   Optional[Any]											= t

      return min_numerator


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