XSLT - Recursive grouping / count based on attribute values - xslt

Question

I'm struggling with a simple recursive count problem based on distinct values. From a list such as:
<List>
<Place continent="Asia" country="India" region="UP">Lucknow</Place>
<Place continent="Europe" country="France" region="Provence">Marseille</Place>
<Place continent="Europe" country="Greece" region="Arcadia">Dimitsana</Place>
<Place continent="Europe" country="Italy" region="Sicily">Sicily</Place>
<Place continent="Asia" country="India" region="Maharastra">Pune</Place>
<Place continent="Asia" country="China">China</Place>
<Place continent="Europe" country="France" region="Provence">Marseille</Place>
<Place continent="America" country="Brasil" region="Pará">Belém</Place>
</List>
I'd like to retrieve an output based on distinct values for the continent, country and region attributes (in some cases optional), that would count recursively each token, as follows:
<Places>
<continent name="America" count="1">
<country name="Brasil" count="1">
<region name="Pará" count="1">
<city name="Belém" count="1"/>
</region>
</country>
</continent>
<continent name="Asia" count="3">
<country name="India" count="2">
<region name="Maharastra" count="1">
<city name="Pune" count="1"/>
</region>
<region name="UP" count="1">
<city name="Lucknow" count="1"/>
</region>
</country>
<country name="China" count="1"/>
</continent>
<continent name="Europe" count="4">
<country name="France" count="2">
<region name="Provence" count="2">
<city name="Marseille" count="2"/>
</region>
</country>
<country name="Greece" count="1">
<region name="Arcadia" count="1">
<city name="Dimitsana" count="1"/>
</region>
</country>
<country name="Italy" count="1">
<region name="Sicily" count="1"/>
</country>
</continent>
I can manage to retrieve each set of distinct values (continents, countries, regions) independently, with, e.g.:
<xsl:template match="List">
<Places>
<xsl:for-each-group select="Place" group-by="#continent">
<continent>
<xsl:attribute name="name">
<xsl:value-of select="#continent"/>
</xsl:attribute>
<xsl:attribute name="count">
<xsl:value-of select="count(current-group())"/>
</xsl:attribute>
</continent>
</xsl:for-each-group>
</Places>
— but, although I suppose I'm missing something very basic, I can't manage to get the nested grouping and count for countries inside continents, etc. Many thanks in advance.