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my $data = [
   [ 'parent1', 'child1a', 'child2a', undef,    ],
   [ 'parent1', 'child1b', 'child2b', 'child3b',],
   [ 'parent1', 'child1c', undef, undef,],
];

my $data = [
   [ 'parent1', 'child1a' ],
...
   [ 'parent1', 'child3b' ],
   [ 'parent1', 'child1c' ],
];

    while (my $row = $sth->fetch()) {
        my ($id, $parent_id) = @$row;
        ...
    }

    while (my $row = $sth->fetch()) {
        my ($parent_id, @children_ids) = @$row;
...
            ...
        }
    }