split and flatten nodes with XSLT

I cannot have any nested spans, so I need to flatten them and concatenate their class attributes so I can track which classes are parents.

Here's a simplified input:

<p>
ZZZ
    <span class="a">
        AAA
        <span class="b">
            BBB
            <span class="c">
                CCC
            </span>
            bbb
        </span>
        aaa
    </span>
</p>

Here's the desired output

<p>
    ZZZ
    <span class="a">
        AAA
    </span>
    <span class="ab">
        BBB
    </span>
    <span class="abc">
        CCC
    </span>
    <span class="ab">
        bbb
    </span>
    <span class="a">
        aaa
    </span>
</p>

Here's the closest I've come (I'm really new to this, so even getting this far took me a long time...)

<xsl:stylesheet version="1.0"
    xmlns:xsl="http://ift.tt/tCZ8VR">
    <xsl:output omit-xml-declaration="yes" indent="yes"/>
    <xsl:strip-space elements="*"/>

    <xsl:template match="/">
        <p>
            <xsl:apply-templates/>
        </p>
    </xsl:template>

    <xsl:template match="*/span">
      <span class='{concat(../../@class,../@class,@class)}'>
           <xsl:value-of select='.'/>
       </span>
       <xsl:apply-templates/>
    </xsl:template>

</xsl:stylesheet>

You can see the result of my failed attempt and how far it is from what I really wanted if you run it yourself. Ideally, I'd like a solution that accepts an arbitrary number of nested levels and can also handle interrupted nests (span, span, notSpan, span...).