Tree-like Checkboxes in AngularJS

I am trying to create a tree-like checkboxes like this :

• o Master Tree -
  • o Tree 1
    • o Subtree 1
    • o Subtree 2
  • o Tree 2
    • o Subtree 1
    • o Subtree 2

where each 'o' is a checkbox and functions include :

1. when a checkbox is clicked to check, all its children checkboxes it will be checked.
2. when a checkbox is clicked to uncheck, all its children checkboxes it will be unchecked
3. when a checkbox is clicked to uncheck, all its parent checkboxes it will be unchecked since it will not be 'select all'

What I've tried:

1. ng-model & ng-changed in all trees - although this is not ideal.

   Select All Below
   Child
   Grandchid 1
   Grandchid 2
   

   Demo

   function Ctrl($scope) {
   $scope.billing_is_shipping = true;
   
   $scope.master = true;
   $scope.child = true;
   $scope.grandchlid = true;
   
   $scope.checked = function (type) {
       switch (type) {
           case 'master':
               $scope.master = !$scope.master;
               if ($scope.master) {
   
                   $scope.child = true;
                   $scope.grandchild = true;
   
               } else {
   
                   $scope.child = false;
                   $scope.grandchild = false;
               }
               $scope.apply();
               break;
           case 'child':
               $scope.child = !$scope.child;
               if ($scope.child) {
                   $scope.grandchild = true;
   
               } else {
                   $scope.grandchild = false;
               }
               $scope.apply();
               break;
   
           case 'grandchild1':
               $scope.grandchild1 = !$scope.grandchild1;
               if(!$scope.grandchild1 || !$scope.grandchild2){
                    $scope.child = false;
                   $scope.master = false;
               }
               break;
   
       }
       console.log($scope.billing_is_shipping)
   }
   

   }

2. ng-model or ng-changed only

   Demo

I've tried $scope.apply() and without but I can only get the first clicks to work and then everything just gives up.

Any approach or help would be greatly appreciated, and thanks in advance.