Public Sports Centers/ Sports Schools in Taipei

I plan to move from Bangkok to Taipei in a few months. I wonder if there is any Taipei equivalent to the mainstay of my existence in Bangkok, the Thai-Japanese Youth Center, a gigantic public gym that costs less than 1.50 USD per year.

Basically I need a place to practice Olympic Style Weightlifting. So that means, at the very least, squat racks and rubber bumpers, like in a fitness center for pro athletes. Probably this kind of facility would be found at some universities, for their intercollegiate teams, or perhaps there is a sports school I could enroll at. A recreational style fitness center will not do. Those places simply aren’t set up for people who use a squat rack for an hour at a time, or need to practise the snatch and the clean and jerk.

Also I would like to find a place that offers gymnastics instruction for adults.

Thanks for any help!

There are public sports centers but they are not as cheap as that.

The important thing is not the price, but the facilities. I have searched the internet for hours and found not one single clue as to where one would go in Taipei to practise olympic lifts. Recreational style fitness centers do not generally allow people to lift weights over their heads and then drop them on the floor over and over again.