German question: Bundesgesundheitsamt

I have a niggly question about German grammar which I
hope is appropriate to ask here.  I was asked why you
add the S's in "Bundesgesundheitsamt."  At first I
thought they were some kind of genitive, ie. der Bund,
des Bundes.  But then Gesundheit is feminine, and
doesn't take an "s", ie. die Gesundheit, der
Gesundheit.  So, where do the S's come from?  I
presume there's a better explanation than simply,
"That's just how it works." Does anyone have a proper
explanation?  TIA,

-Weiben Wang

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