xslt remove record based on criteria and groupBy

I'm struggling with a difficult xsl transformation and I can't figure out how to make it work. As input I have a record collection. Each record is identified by two keys (pk1 and pk2) and it has a qualifier. The goal is copying those records grouped by pk1 and pk2. And this is simple. The problem comes when I have to copy only those where the occurrences of qualifier A and B are the same. Here is the input file.

<Data>
<!-- first case -->
<record>
    <pk1>0001</pk1>
    <pk2>AAA</pk2>
    <quantity>50.00</quantity>
    <qualifier>A</qualifier>
</record>
<!-- second case -->
<record>
    <pk1>0002</pk1>
    <pk2>AAA</pk2>
    <quantity>10.00</quantity>
    <qualifier>A</qualifier>
</record>
<record>
    <pk1>0002</pk1>
    <pk2>AAA</pk2>
    <quantity>10.00</quantity>
    <qualifier>B</qualifier>
</record>
<record>
    <pk1>0002</pk1>
    <pk2>BBB</pk2>
    <quantity>15.00</quantity>
    <qualifier>A</qualifier>
</record>
<!-- third case -->
<record>
    <pk1>0003</pk1>
    <pk2>AAA</pk2>
    <quantity>20.00</quantity>
    <qualifier>A</qualifier>
</record>
<record>
    <pk1>0003</pk1>
    <pk2>AAA</pk2>
    <quantity>20.00</quantity>
    <qualifier>B</qualifier>
</record>
<record>
    <pk1>0003</pk1>
    <pk2>AAA</pk2>
    <quantity>20.00</quantity>
    <qualifier>A</qualifier>
</record>
<record>
    <pk1>0003</pk1>
    <pk2>BBB</pk2>
    <quantity>70.00</quantity>
    <qualifier>A</qualifier>
</record>
<record>
    <pk1>0003</pk1>
    <pk2>BBB</pk2>
    <quantity>70.00</quantity>
    <qualifier>B</qualifier>
</record>
<!-- fourth case -->
<record>
    <pk1>0004</pk1>
    <pk2>AAA</pk2>
    <quantity>100.00</quantity>
    <qualifier>B</qualifier>
</record>

And this is the expected output.

<Data>
<!-- first case -->
<!-- second case -->
<record>
    <pk1>0002</pk1>
    <pk2>AAA</pk2>
    <quantity>10.00</quantity>
    <qualifier>A</qualifier>
</record>
<!-- third case -->
<record>
    <pk1>0003</pk1>
    <pk2>BBB</pk2>
    <quantity>70.00</quantity>
    <qualifier>A</qualifier>
</record>
<!-- fourth case -->

The explanation for each case is: First Case: 0001|AAA|A doesn't have its pair 0001|AAA|B -> remove

Second Case: 0002|AAA|A has its pair 0002|AAA|B -> keep the "A" one

Third Case: 0003|AAA|A has its pair 0003|AAA|B but there's one more 0003|AAA|A, which means for this group "A"s are not the same occurrences of "B"s -> remove

Third Case: 0003|BBB|A has its pair 0003|BBB|B -> keep the "A" one

Fourth case: 0004|AAA|A doesn't have its pair 0004|AAA|B -> remove

As I said, I don't know how to achieve and wheter it's doable with xslt. Could you please help me? Thank you.