use strict;
use warnings;

open my $file, '<', 'input.txt' or die $!;

process_file($file);

exit 0;

sub process_file {
    my ($fh) = @_;

    while ( my $line = <$fh> ) {
        print $line;

        if ( $line =~ /section start marker/ ) {
            $line = handle_section($fh);
            redo if defined $line;
        }
    }
}

sub handle_section {
    my ($fh) = @_;
    my ( @entries, $line );

    while ( $line = <$fh> ) {
        last unless $line =~ m{
            ( [^(]+ ) # 1 anything except opening paren
            \s        #   space
            \(        #   opening paren
            ( \d+   ) # 2 number
        }x;

        push @entries, [ pack( 'Na*', $2, $1 ), $line ];
    }

    print map  { $_->[1] }
          sort { $a->[0] cmp $b->[0] } @entries;

    return $line;
}