Since others already gave you good general purpose suggestions...

#!/usr/bin/perl -l

use strict;
use warnings;

my @fh=map {
    open my $fh, '<', $_ or die "Can't open `$_': $!\n";
    $fh } @ARGV;

while (@fh) {
    @fh=grep !eof $_, @fh;
    print map { chomp(my $line=<$_>); $line } @fh;
}

__END__
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