There has been other good replies already, so I'll leave it with that. Except there is (at least) one thing that everyone seem to have overlooked.

The $ct variable is increased for every hit, or more interestingly, for each time @files is increased. So that can be replaced by

  $ct -= @files;
  while (my $line = <F>) { ... } # Old code without $ct
  $ct += @files;
[download]

HTH,
ihb