A shape is produced by the following process:

• A semicircle of radius $1$ is drawn.

• A semicircle whose diameter lies along the radius of the first semicircle is removed.

• A semicircle whose diameter lies along the radius of the second semicircle is replaced

• A semicircle whose diameter lies along the radius of the third semicircle is removed

and so on.

The shape produced after $6$ steps is shown below:

If this process is repeated infinitely, what is the area of the resulting shape?