An Apollonian gasket is formed by the following steps:

Step 1: Draw three circles that are tangent to each other, forming one triangle with curved sides, as shown in the figure.

Step 2: Draw a circle that is tangent to the three circles, forming three triangles with curved sides.

Step 3: Draw three circles, making each one tangent to the new circle and to two of the original circles, forming nine triangles with curved sides.

Continue the steps by drawing circles that are tangent to three circles and form three triangles with curved sides.

How many curved triangles are in the ninth iteration?