[Inkscape-user] divide overlapping objects

If I have three overlapping objects (closed paths), is there a easy way to 'split them up'/divide them using the borders where they intersect?

The 'boolean operations' seem to either divide one object by the other, removing the top-most one, *or* cut the path (outline) of one using the other.

Conceptually, if I got three cirlcles, each one overlapping partially all the others, after this operation, I'd like to end up with 7 separated parts.

Thanks!