Convert parent-child array to tree

Can anyone help converting the following list of parent-child objects:

[
   {
      "name":"root",
      "_id":"root_id",
   },
   {
      "name":"a1",
      "parentAreaRef":{
         "id":"root_id",
      },
      "_id":"a1_id",
   },
   {
      "name":"a2",
      "parentAreaRef":{
         "id":"a1_id",
      },
      "_id":"a2_id",
   },
   {
      "name":"a3",
      "parentAreaRef":{
         "id":"a2_id",
      },
      "_id":"a3_id",
   },
   {
      "name":"b1",
      "parentAreaRef":{
         "id":"root_id",
      },
      "_id":"b1_id",
   },
   {
      "name":"b2",
      "parentAreaRef":{
         "id":"b1_id",
      },
      "_id":"b2_id",
   },
   {
      "name":"b3",
      "parentAreaRef":{
         "id":"b1_id",
      },
      "_id":"b3_id",
   }
]

into a tree structure showing the parent-child relationship:

[
    {
        "name": "root",
        "_id":"root_id",
        "children": [
            {
                "name": "a1",
                "_id":"a1_id",
                "children" : [
                    {
                        "name" : "a2",
                        "_id":"a2_id",
                        "children" : [
                            {
                                "name" : "a3"
                                "_id":"a3_id"
                            }
                        ]
                    }
                ]
            }, 
            {
                "name": "b1",
                "_id":"b1_id",
                "children" : [
                    {
                        "name" : "b2"
                        "_id":"b2_id"
                    },
                    {
                        "name" : "b3"
                        "_id":"b3_id"
                    }
                ]
            }
        ]
    }
]

(The output structure is an array to allow for multiple roots but if we can get a solution that handles a single root that's great too.)

The output tree lo