You do realize that not eating isn't going to help you at all?
If you want to lose weight, naturally not eating will make you achieve that. But by doing that you are becoming anorexic. Your metabolism will get slower, and when you start eating again, and will gain all that weight back as well as some extra.
If you just starve yourself, your body will become accustomed to the low calory intake and will use anything you eat to turn it into fat - so honestly if what you want is to lose weight that is not the method you should use.
Not only that, but being at a BMI of 21 is a perfectly healthy weight, why would you want to be underweight? Being skinny doesn't really make one more attractive.
Maybe what you should do is do plenty of exercise and get in shape - which will help losing any weight if you really do have any excess weight (which I doubt), will make you feel more energetic and thus happier about yourself - as well as giving your body some nice definition.
In any case, you don't want to lose 18 kgs - are you crazy? 56 - 18 = 38 kgs. That weight is not even adequate for someone 20cms beneath your height. At your height I would definitely not go beneath 48 kgs, and even that weight is pushing it on the very light side. I would say, stick to the weight you are and tone up.