




def      __lowerCAmelCase			(					UpperCamelCase = 1000000      )     ->	int:
		lowerCAmelCase__				:  Optional[int]		       =     [i - 1 for i in range(limit + 1      )]

		for i in range(2	,      limit + 1      ):
				if phi[i] == i - 1:
						for j in range(2 * i	,      limit + 1	,      UpperCamelCase      ):
								phi[j] -= phi[j] // i

		return sum(phi[2 : limit + 1]      )


if __name__ == "__main__":
					print(solution())







import math



def      __lowerCAmelCase			(					UpperCamelCase	,      UpperCamelCase      )     ->	float:
  if (
      not isinstance(UpperCamelCase	,      (int, float)      )
      or power_factor < -1
      or power_factor > 1
  ):
    raise ValueError('''power_factor must be a valid float value between -1 and 1.'''      )
  return apparent_power * power_factor



def      __lowerCAmelCase			(					UpperCamelCase	,      UpperCamelCase      )     ->	float:
  if (
      not isinstance(UpperCamelCase	,      (int, float)      )
      or power_factor < -1
      or power_factor > 1
  ):
    raise ValueError('''power_factor must be a valid float value between -1 and 1.'''      )
  return apparent_power * math.sqrt(1 - power_factor**2      )


if __name__ == "__main__":
     import doctest

     doctest.testmod()

