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use 5.14;
use Sort::Key qw(keysort);
my @sorted = keysort { s/[^aeiou]+//gr } @data;

use Sort::Key qw(keysort);
my @sorted = keysort { join '', /[aeiou]+/g } @data;

my %keys;
$key{$_} = s/[^aeiou]+//gr for @data;
my @sorted = sort { $key{$a} cmp $key{$b} } @data;