




def      __lowerCAmelCase			(					UpperCamelCase = 10      )     ->	str:
  if not isinstance(UpperCamelCase	,      UpperCamelCase      ) or n < 0:
    raise ValueError('''Invalid input'''      )
  lowerCAmelCase__				:  int		       =     10**n
  lowerCAmelCase__				:  Tuple		       =     28433 * (pow(2	,      7830457	,      UpperCamelCase      )) + 1
  return str(number % modulus      )


if __name__ == "__main__":
     from doctest import testmod

     testmod()
     print(F"""{solution(10) = }""")







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()

