Counting Duplicates in XSLT 2.0

Hello everyone!

I have an element with a large number of complex child-elements and for
each child I want to know how many duplicates there are (considering two
elements as identical iff they are deep-equal). Initially I thought 

  <for-each-group group-by="."> ... 

to be the way to go, but then I noticed in the XSLT 2.0 spec that the
value of the group-by expression is atomized after evaluation. So, how
do I go about this task?

Going further:

* How can I remove all the duplicates of a given child element,  
  retaining exactly one copy?
* How can I keep exactly one copy iff the number of identical copies is 
  odd, and remove all copies iff the number is even?


Thanks,
Felix