Use a hash...it's good at counting arbitrary numbers of arbitrary things:

my $recordfile = "/foo/bar/copy.txt";
my %record;
open (FILE, "$recordfile") or die "Can't open $recordfile: $!\n";
while(<FILE>) {
  if (/^(..)/) {
    $record{$1}++;
  }
}
print "The Total number or records = $.\n\n";
for (sort keys %record) {
  print "$_ reports $record{$_} records.\n";
}

## Or, to output the records from fewest to most:
for (sort {$record{$a} <=> $record{$b} or $a cmp $b} keys %record) {
  print "$_ reports $record{$_} records.\n";
}
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