




'''simple docstring'''



def   lowercase__(			__UpperCamelCase:					int = 1_00_00_00    ):

      """simple docstring"""






      SCREAMING_SNAKE_CASE   :      Tuple    					=						set(range(3      ,__UpperCamelCase      ,2    )    )
      primes.add(2    )
      for p in range(3      ,__UpperCamelCase      ,2    ):
            if p not in primes:
                  continue
            primes.difference_update(set(range(p * p      ,__UpperCamelCase      ,__UpperCamelCase    )    )    )

      SCREAMING_SNAKE_CASE   :      Any    					=						[float(__UpperCamelCase    ) for n in range(limit + 1    )]

      for p in primes:
            for n in range(__UpperCamelCase      ,limit + 1      ,__UpperCamelCase    ):
                  phi[n] *= 1 - 1 / p

      return int(sum(phi[2:]    )    )


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








'''simple docstring'''



def   lowercase__(			__UpperCamelCase:					int    ):

      """simple docstring"""






      if not isinstance(__UpperCamelCase      ,__UpperCamelCase    ):
            raise TypeError('Input value must be an \'int\' type'    )

      SCREAMING_SNAKE_CASE   :      int    					=						0
      while number:
            position += 1
            number >>= 1

      return position


if __name__ == "__main__":
      import doctest

      doctest.testmod()


