


'''simple docstring'''
import math



def 				lowerCAmelCase__	(       UpperCAmelCase     ):






       """simple docstring"""





       if n <= 0:
              raise ValueError("""Only positive integers have prime factors"""     )
       snake_case__					:	Union[str, Any]          =					[]
       while n % 2 == 0:
              pf.append(2     )
              snake_case__					:	List[str]          =					int(n / 2     )
       for i in range(3    ,       int(math.sqrt(UpperCAmelCase     )     ) + 1    ,       2     ):
              while n % i == 0:
                     pf.append(UpperCAmelCase     )
                     snake_case__					:	Optional[Any]          =					int(n / i     )
       if n > 2:
              pf.append(UpperCAmelCase     )
       return pf



def 				lowerCAmelCase__	(       UpperCAmelCase     ):






       """simple docstring"""





       if n <= 0:
              raise ValueError("""Only positive numbers are accepted"""     )
       snake_case__					:	Optional[int]          =					1
       snake_case__					:	Tuple          =					1
       while n % 2 == 0:
              temp += 1
              snake_case__					:	Union[str, Any]          =					int(n / 2     )
       div *= temp
       for i in range(3    ,       int(math.sqrt(UpperCAmelCase     )     ) + 1    ,       2     ):
              snake_case__					:	Any          =					1
              while n % i == 0:
                     temp += 1
                     snake_case__					:	Dict          =					int(n / i     )
              div *= temp
       if n > 1:
              div *= 2
       return div



def 				lowerCAmelCase__	(       UpperCAmelCase     ):






       """simple docstring"""





       if n <= 0:
              raise ValueError("""Only positive numbers are accepted"""     )
       snake_case__					:	Optional[int]          =					1
       snake_case__					:	List[str]          =					1
       while n % 2 == 0:
              temp += 1
              snake_case__					:	int          =					int(n / 2     )
       if temp > 1:
              s *= (2**temp - 1) / (2 - 1)
       for i in range(3    ,       int(math.sqrt(UpperCAmelCase     )     ) + 1    ,       2     ):
              snake_case__					:	Tuple          =					1
              while n % i == 0:
                     temp += 1
                     snake_case__					:	Any          =					int(n / i     )
              if temp > 1:
                     s *= (i**temp - 1) / (i - 1)
       return int(UpperCAmelCase     )



def 				lowerCAmelCase__	(       UpperCAmelCase     ):






       """simple docstring"""





       snake_case__					:	Any          =					n
       for x in set(prime_factors(UpperCAmelCase     )     ):
              s *= (x - 1) / x
       return int(UpperCAmelCase     )


if __name__ == "__main__":
     import doctest

     doctest.testmod()








def   snake_case_	(    snake_case	)    ->							str:
       lowercase__:  Optional[Any]         =  1
       lowercase__:  Optional[Any]         =  0
       lowercase__:  int         =  1
       lowercase__:  Any         =  1
       lowercase__:  Optional[Any]         =  3
       lowercase__:  List[str]         =  3
       lowercase__:  Optional[Any]         =  limit
       lowercase__:  List[Any]         =  0

       lowercase__:  int         =  ''
       while counter != decimal + 1:
              if 4 * q + r - t < n * t:
                     result += str(snake_case	)
                     if counter == 0:
                            result += "."

                     if decimal == counter:
                            break

                     counter += 1
                     lowercase__:  List[Any]         =  10 * (r - n * t)
                     lowercase__:  int         =  ((10 * (3 * q + r)) // t) - 10 * n
                     q *= 10
                     lowercase__:  Any         =  nr
              else:
                     lowercase__:  List[str]         =  (2 * q + r) * l
                     lowercase__:  Tuple         =  (q * (7 * k) + 2 + (r * l)) // (t * l)
                     q *= k
                     t *= l
                     l += 2
                     k += 1
                     lowercase__:  Dict         =  nn
                     lowercase__:  Optional[int]         =  nr
       return result




def   snake_case_	(    )    ->							None:
       print(f'{calculate_pi(50	) = }'	)
       import doctest

       doctest.testmod()


if __name__ == "__main__":
 main()


