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my $valid = join "|", @valid;
print "okay" if /^$valid$/;

# don't run this code on every match: the idea is the qr// needs
# to be computed only once.
...
# now match as many times as you like.
print "$_: " . (/$valid_re/ ? "okay" : "not okay") . "\n"
        for @a_bunch_of_inputs;