Sum of multiple elements

I have an instance document, input.xml below, that I have to perform a
sum on multiple elements.  As you can see in my instance document, I
perform the sum function with the 'count' element.  I believe this is
going to mainly be a grouping problem.

I need to sum all of:
* Sex, Grade, Race - (All males, in grade 01, of race HI)
* Sex, Grade - (All males in grade 01)
* Sex, Race - (All males of race HI)
* Grade, Race - (Everybody of race HI in grade 01)

These totals are repeated for about 15 grades, and 6 races, and of
course once for male and another time for females.  So 15 * 6 = 90 ...
90 * 2 = 180 combinations.  You can see where my concern lies.

My instance document can be as large as (or possibly even larger than)
20MB.  So with a document that big and with all the combinations ...
well ... I'm just plain scared :)

I would like to open the door for suggestions on the best way to
handle this.  I would assume this is best left up to something such as
a DBMS, but I am currently stuck with this scenario.  I do also have
access to the schema, so reading the possible values from a schema is
also an option instead of traversing the document.

The project will be a C# 2.0 app, but for testing and developing of
the transform I am using xalan 1.10.0 with xerces 2.7.0 ... so no XSLT
2.0 possible.

input.xml
====================
<?xml version="1.0" ?>
<data xmlns="http://schemas.somewhere.com/class.xsd">
<district num="1234">
  <local num="1234-12">
    <class>
      <grade>01</grade>
      <race>HI</race>
      <gender>M</gender>
      <count>26</count>
    </class>
    <class>
      <grade>PK</grade>
      <race>AM</race>
      <gender>M</gender>
      <count>2</count>
    </class>
  </local>
  <local num="1234-12">
    <class>
      <grade>KG</grade>
      <race>HI</race>
      <gender>F</gender>
      <count>21</count>
    </class>
    <class>
      <grade>KG</grade>
      <race>HI</race>
      <gender>F</gender>
      <count>7</count>
    </class>
  </local>
</district>
</data>