Oy, young people these days! Always with the hashes it is. Like memory grows on trees! When I was your age, we had no RAM. We had 4K of core and we were thankful for it!

Since the input is sorted, you just need one record of "lookahead":

use strict;
my $prev;
my $dup=0;
my ($ifile, $ufile, $dupfile) = qw(data uniq dups);

open(IN, $ifile) or die "Cannot open $ifile: $!\n";
open(UNQ,">", $ufile) or die "Cannot open $ufile: $!\n";
open(DUP, ">", $dupfile) or die "Cannot open $dupfile: $!\n";

while (<IN>) {
  if (defined($prev)) {
    if ($prev eq $_) {
      $dup = 1;
      print DUP $prev;
    } else {
      if ($dup) {
    print DUP $prev;
    $dup = 0;
      } else {
    print UNQ $prev;
      }
    }
  }
  $prev = $_;
}
  if (defined($prev)) {
      if ($dup) {
    print DUP $prev;
    $dup = 0;
      } else {
    print UNQ $prev;
      }
  }
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