Aggregate by the highest count

How can I aggregate results by the highest count using aggregation framework?

{
  "type": "dog",
  "name": "buddy",
  "count": 67
},
{
  "type": "dog",
  "name": "buddy",
  "count": 34
},
{
  "type": "dog",
  "name": "tucker",
  "count": 17
},
{
  "type": "dog",
  "name": "tucker",
  "count": 52
},
{
  "type": "cat",
  "name": "gizmo",
  "count": 11
}

I'm trying to aggregate the results from above, so if the dog has the same name I would like to get the one with the highest count. So it will look like:

{
  "type": "dog",
  "name": "buddy",
  "count": 67
},
{
  "type": "dog",
  "name": "tucker",
  "count": 52
},
{
  "type": "cat",
  "name": "gizmo",
  "count": 11
}

I have tried using $group for that, but don't really know how I would distinct the results by the highest count.

Sort all the docs by count descending and then take first count from each grouping of type and name:

db.test.aggregate([
    {$sort: {count: -1}},
    {$group: {_id: {type: '$type', name: '$name'}, count: {$first: '$count'}}}
])

Output:

{
    "result" : [ 
        {
            "_id" : {
                "type" : "cat",
                "name" : "gizmo"
            },
            "count" : 11
        }, 
        {
            "_id" : {
                "type" : "dog",
                "name" : "tucker"
            },
            "count" : 52
        }, 
        {
            "_id" : {
                "type" : "dog",
                "name" : "buddy"
            },
            "count" : 67
        }
    ],
    "ok" : 1
}