SED - Print - Print paragraph if it contains string1 and string2 and string3 (in any order)

Print paragraph if it contains AAA and BBB and CCC (in any order).

sed -e '/./{H;$!d;}' -e 'x;/AAA/!d;/BBB/!d;/CCC/!d'

NOTE: HHsed v1.5 must insert a 'G;' after 'x;'