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my @sorted =
   map  { $_->[0] }
   sort { $a->[1] cmp $b->[1] } # or <=>, or $b before $a
   map  { [$_, f($_)] }
   @unsorted;

# the first map does this
qw(8 11 9 4 3) --> (
...
  [ 4, "vi"],
  [ 3, "iii"],
)

# the sort does this:
(
...
  [ 8, "viii"],
  [11, "xi"],
)

(
  [ 3, "iii"],
...
  [ 8, "viii"],
  [11, "xi"],
) --> qw( 3 9 4 8 11 )

use strict;
use warnings;
...

__END__ # output shown below
3 4 9 8 11

my @sorted = sort { f($a) cmp f($b) } @unsorted;

*f = sub {
    $::count++;
    END { print "f() called $::count times\n" };
    goto \&Roman::roman;
};

use List::Util "shuffle";
my @unsorted = shuffle(1..100);