




def       __lowerCamelCase							(     __UpperCamelCase)    ->  list:
     a											=   [True for i in range(n + 1)]
     a											=   [i - 1 for i in range(n + 1)]
     a											=   []
     for i in range(2	,      n + 1):
          if is_prime[i]:
               primes.append(__UpperCamelCase)
          for j in range(0	,      len(__UpperCamelCase)):
               if i * primes[j] >= n:
                    break
               a											=   False

               if i % primes[j] == 0:
                    a											=   totients[i] * primes[j]
                    break

               a											=   totients[i] * (primes[j] - 1)

     return totients


if __name__ == "__main__":
   import doctest

   doctest.testmod()







from __future__ import annotations

def       SCREAMING_SNAKE_CASE							(     __UpperCamelCase)    ->  int | None:
     for r in range(1	,      __UpperCamelCase):
          a											=   []
          for x in range(n - 1):
               a											=   pow(__UpperCamelCase	,      __UpperCamelCase	,      __UpperCamelCase)
               if val in li:
                    break
               li.append(__UpperCamelCase)
          else:
               return r
     return None


if __name__ == "__main__":
   lowercase__   :    Tuple 					=      int(input("Enter a prime number q: "))
   lowercase__   :    List[Any] 					=      find_primitive(q)
   if a is None:
      print(F'Cannot find the primitive for the value: {a!r}')
   else:
      lowercase__   :    Any 					=      int(input("Enter private key of A: "))
      lowercase__   :    Optional[int] 					=      pow(a, a_private, q)
      lowercase__   :    Optional[Any] 					=      int(input("Enter private key of B: "))
      lowercase__   :    Any 					=      pow(a, b_private, q)

      lowercase__   :    Optional[Any] 					=      pow(b_public, a_private, q)
      lowercase__   :    List[str] 					=      pow(a_public, b_private, q)

      print("The key value generated by A is: ", a_secret)
      print("The key value generated by B is: ", b_secret)

