sub stats {
    my %hhp = @_;
    
    my $keyCounter = {}; # a counter hash of which keys are used at level two
    my $statCounter = {}; # a counter for the actual values
    
    foreach my $key1 (keys %hhp) {
        my @cList = ();
        foreach my $key2 (sort keys %{$hhp{$key1}}) {
           push(@cList,$key2);
           my $statKey = sprintf("%s->%s=%s",$key1,$key2,$hhp{$key1}{$key2});
           ++ $$statCounter{$statKey}; # make statistical entry on value
        }
        ++ $$keyCounter{join('+',@cList)}; # make statistical entry on key2
        
    }
    return ($keyCounter,$statCounter);
}

#### main
my ($keyResult,$statResult) = stats(%hash);

foreach my $hash ($keyResult,$statResult){
    foreach my $key (sort keys %$hash){
        print "$key $$hash{$key}\n";
    }
}
                       
__END__

## the result
x 1
x+y+z 1
x+z 1
y+z 1
a->x=40 1
a->z=102 1
b->x=10 1
b->y=20 1
b->z=100 1
c->x=50 1
d->y=30 1
d->z=101 1