How to Create a Vertically Spanned Cell in a Second Column in Table?

Question

I want to get the following table:

 +---+---+---+
 |   | b | c |
 |   +---+---+
 | a |   | c |
 |   + b +---+
 |   |   | c |
 +---+---+---+

but I can't seem to make it happen. The closest I got was with the following:

.TS
tab(^) allbox;
l l l
^ l l
^ ^ l.
a^b^c
^b^c
^^c
.TE

Which produced the following table:

   +--+---+---+
   |  | b | c |
   |  +---+---+
   |a | b | c |
   |  +---+---+
   |  |   | c |
   +--+---+---+

Answer 1

The following seems to have done the trick.

.TS
tab(@) allbox;
l l l
^ l l
^ ^ l.
a@b@c
@b@c
@@c
.TE

Something in the tools I used seem to be confusing the separator ^ and the vertical span format.