Where did that phrase come from? Letting the cat out of the bag

We're all familiar with this phrase but where did it come from?

Back in the olden days, people would sell piglets in a bag. But some dishonest merchants would try to deceive its buyers by putting a cat in the bag instead of a pig. However, if the cat was discovered the jig was up and "the cat was out of the bag"

And now you know!