Counting countries

Trying to count the number of countries in a MySQL database. 
Each client has a country entered, and we want to add the total
countries we are in and display on our site.
The following code is not working correctly. 
Any help appreciated.....

$SQL =<<SQL;
select count(distinct(country)), country as total3 from $tablename
SQL
$sth = $dbh->prepare($SQL);
if(!$sth) { die("Error: " . $dbh->errstr . "\n"); }
if(!$sth->execute) { die("Error: " . $sth->errstr . "\n"); }

$match = 0;
if($sth->rows != 0)
{
$total_rows = $sth->rows;
$match = 1;

for ($counter = 0; $counter < $total_rows; $counter++)
{
my($ref) = $sth->fetchrow_hashref;

$totalcountries = $ref->{'total3'};

open(NUM,">$data_directory/country_count.txt");
flock (NUM, 2);
print NUM "$totalcountries";
close(NUM);
}
}
$sth->finish();






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