"""simple docstring"""





from math import loga





def 				a_     (      _lowerCAmelCase  : int     ):





       '''simple docstring'''

       if a < 0:
              raise ValueError('Input value must be a positive integer'     )
       elif isinstance(_lowerCAmelCase   , _lowerCAmelCase     ):
              raise TypeError('Input value must be a \'int\' type'     )
       return 0 if (a == 0) else int(loga(a & -a     )     )


if __name__ == "__main__":
       import doctest

       doctest.testmod()





def 				__lowerCamelCase						( UpperCAmelCase_						:		int = 100_0000						):




      """simple docstring"""





      a						:Any 							=       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_						)						)						)

      a						:Union[str, 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() = }""")





