I'm a MongoDB noob and I have a MongoDB collection with millions of documents, each with tens of keys (average ~ 60, large variance) from a set of around 100.  I'd like to get a count of each key across the entire collection.

For example, if the documents in the collection were:
```json
{"_id":0, "foo": 0, "bar":1, "baz":2}
{"_id":1, "foo": 0, "baz":7, "qux":11, "quux":13}
{"_id":2, "foo": 1, "bar":1, "quux":3}
```
then the desired output would be:
```json
{"_id":3, "foo":3, "bar":2, "baz":2, "qux":1, "quux": 2}
```
I can "explode" the collection with `$objectToArray`, `$unwind`, `$group`, and then `$count`, but it's slow.

Is there something that could do this efficiently in one pass through the collection?  Something like,
```
[notional psuedocode]
output={}
foreach document:
  foreach key:
    if output.key exists:
      output.key+=1
    else:
      output.key=1

=> output: {key1: key1_value, ...}
```