Connected curves puzzle (20 pieces)

A puzzle similar to a 14 piece puzzle that I posted in another printable. You can find more of the theory in that write-up.

The puzzle consists of 20 semicircles that snap together. Each semicircle has a set of three curves than can be pair with another, either as one simple closed curve or as separated curves including one with a hole.

The shapes are based on parentheses matching as described in the previous printable. There are actually 42 shapes that can be made with 5 matching pairs of parentheses, but these are the 20 that split up into 3 disconnected curves on each half.

The sum of the components must be 6 to form a single connected curve, though this is not a sufficient condition. So if the other cases had been included, we would need to match 2 components with 4 component halves, as well as the single 1 and 5 component tiles.

Selecting just this subset reduces the complexity while eliminating the obvious reasoning based on component count.

The 20 models are not numbered in any particular order or labeled. They snap together and can be printed in two colors by switching the filament as I did for most of them. The more craft-minded may consider painting them as I did in my last photo.

The solution shown as the cover photo is only one of many possibilities.