my $equation=`type postfix.txt`;
my @postfix = split /,/,$equation;
$|=1;

## MULTIPLY THROUGH   ###############################################
my @result;
my $idxresult=0;
for ( my $j=0; $j<=$#postfix; $j++) {
  my $a=$postfix[$j];
printf("\n\n$j of $#postfix %02.2f\n",($j/$#postfix)*100);
  my $result;
  if ($a eq 'x' ) {
print "Multiply top 2 through:";
  print "BEFORE STACK:\n";
  for (my $j=$idxresult; $j>0; $j--) {
    print "  $j: ",length($result[$j]),"\n";
#   print "  $j: $result[$j]\n";
  }
    my @r1=split /\+/, $result[$idxresult--];
    my @r2=split /\+/, $result[$idxresult];
    my $mcnt = scalar @r1 * scalar @r2;
print "$mcnt ",scalar @r1, " X ", scalar @r2, "\n";
#print "$mcnt (@r1) BY (@r2)\n";
    my @tmpresult;  ## ARRAY METHOD 60 TO 1 FASTER THAN SINGLE STRING
    my $t2=0; 
    foreach my $r1 (@r1) {
      foreach my $r2 (@r2) {
        $tmpresult[$t2]= "$r2,$r1";
	$t2++;
      }
    }
#print "RESULT STACK $idxresult",length($result[$idxresult]);
  print "AFTER STACK:\n";
  for (my $j=$idxresult; $j>0; $j--) {
    print "  $j: ",length($result[$j]),"\n";
#   print "  $j: $result[$j]\n";
  }
print "ELEMENTS: $#tmpresult\n";
### vvvvvv ##THE JOIN BELOW FAILS ####
    $result= join('+',@tmpresult);
### ^^^^^  ## THE JOIN ABOVE FAILS ####
    $result[$idxresult]=$result;
    delete($result[$idxresult+1]);
  } elsif ($a eq '+' ) {
print "+ LINK TOP 2 ELEMENTS\n";
    $idxresult--;
    $result[$idxresult].= '+' . "$result[$idxresult+1]";
  } elsif ( $a =~ /\d+/ ) {
print "ADD VAR: $a\n";
    $idxresult++;
    $result[$idxresult]=$a;
  }
  print "STACK:\n";
  for (my $j=$idxresult; $j>0; $j--) {
    print "  $j: ",length($result[$j]),"\n";
#   print "  $j: $result[$j]\n";
  }
# if ($j % int($#prefix * .01) == 0) {
#   printf("\n\nProcessed:%d\%\n",int(($j/$#prefix)*100));
# }
}
if ($idxresult != 1 ) {
  print "E: Not everything processed. $idxresult items in the stack.\n";
}

print "ALL PATHS FORM: $result[$idxresult]\n";