my %h; # the inverted hash
  for my $de ( keys %{ $hash{A}{B}{C} } ) { # gives D, E
    for my $k ( keys %{ $hash{A}{B}{C}{$de} } ) {
      $h{$k}{$de} = $hash{A}{B}{C}{$de}{$k};
    }
  }

  # now print it out:
  for my $k ( sort keys %h ) {
    for my $de ( sort keys %{$h{$k}} ) {
      print "$k = $h{$k}{$de} (from $de)\n";
    }
  }