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#!/usr/bin/env perl

...
close $data_fh;

print for @output;

123 string 1
111 string 1
...
777 string 3
888 string 3
999 string 3

123 string 1
111 string 1

111 string 1
123 string 1

123 string 4
111 string 4

while (<$ref_fh>) {
    chomp;
...
    next unless $ref_left{$left} or $ref_right{$right};
    ++$ref_right{$right};
}