my $mask = "";
my %seen;
for(my $i=0; $i<@AllArraysIHave; ++$i) {
  vec($mask, $i, 1) = 1;
  foreach my $item (@{$AllArraysIHave[$i]}) {
    $seen{$item} = "" unless exists($seen{$item});
    vec($seen{$item}, $i, 1) = 1;
  }
}
my @all_there = grep $seen{$_} eq $mask, keys(%seen);