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use List::MoreUtils qw(part);
use constant NWAYS => 3;
...
my $i;
#my @AoA = part { $i++ % NWAYS } keys %hash;
my @AoH = map +{map {$_ => $hash{$_}} @$_}, part { $i++ % NWAYS } keys
+ %hash;

use 5.020;
my @AoH = map +{ %hash{@$_} }, part { $i++ % NWAYS } keys %hash;