SPARQL query "Which states of the USA share borders with the max number of states?"

I would like to ask wikidata the following question: "Which states of the USA share borders with the max number of states?"

I tried the query below. With the subquery (lines 8-19) I get the maximum number of borders of any US state (?max_bs). And it works, it results to be 8. Then with the outer SELECT I would like to get only those US states with number of borders equal to ?max_bs. But is does not work as I expected.

SELECT ?state WHERE {
  ?state wdt:P31 ?z1 .
  ?z1 wdt:P279* wd:Q35657 .
  ?state wdt:P47 ?borders1 .
  ?borders1 wdt:P31 ?w1 .
  ?w1 wdt:P279* wd:Q106458883 .
  {
   SELECT (MAX(?bs) aS ?max_bs) WHERE {
   {
     SELECT ?state (COUNT(?borders) AS ?bs) WHERE {
       ?state wdt:P31 ?z .
       ?z wdt:P279* wd:Q35657 .
       ?state wdt:P47 ?borders .
       ?borders wdt:P31 ?w .
       ?w wdt:P279* wd:Q106458883
     }
     GROUP BY ?state
   }
  }
 }
}
GROUP BY ?state
HAVING(COUNT(?borders1) = (?max_bs))