Each line you read in during your input loop has a newline character at the end. Use chomp to take it off.
while(<DATA>){
chomp;
my $line = $_;
$faclist{$line} = "";
}
After that, I think it should work.
Update: I notice also that this line:
if exists $faclist{$i}{#THIS IS WHERE THE PROBLEM IS
...has a syntax error. It should be:
if ( exists $faclist{$i} ) {#THIS IS WHERE THE PROBLEM IS
Note the parentheses.
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