Problem with select all tri-state checkboxes

I have a list of checkboxes - two parents and each parent has 5 childs. The parents should have 3 states (checked,unchecked,indeterminate). Right now, my code is working BUT I'm trying to add a 'select all' checkbox , which will select the two parents and all their childs.

What I tried to do is adding one more label above:

    <label>
    <input type="checkbox" data-indeterminate-checkbox data-child- 
     list="model.people" data-property="eaten" data-ng- 
     model="model.allEaten"> All eaten
    </label>

but it's not working - the checkbox is not acting as expected.

Full code: http://jsfiddle.net/wnjze03h/210/