Can mongo group by array element fully utilize index? - arrays

Question

I have some data in mongo looks like
{ "name": "John", "city":"X", "location": ["A", "B"] }
{ "name": "Dude", "city":"X", "location": ["B"] }
{ "name": "Alan", "city":"Y", "location": ["A", "B"] }
{ "name": "Wang", "city":"Y", "location": ["X", "B"] }
There is a compound index
{
"city": 1,
"location": 1
}
This index is use to speed up query for names in specific city and location like
db.collection.find( { "city":"X", location: "A" } )
db.collection.find( { "city":"Y", location: { $in: ["A", "B"] } } )
What I want to do is to know how many rows exists for each location in a specific city, say X. With above data the result should be:
{ "_id": { "location":"A" }, amount: 1 }
{ "_id": { "location":"B" }, amount: 2 }
Here assumes that I do not know how many type of location it is. I mean I can not list all possible location elements before I query it.
If I know all possible locations and it is not too much, a simple thought is to issue multiple query and each of the query can fully utilize index without fetch any data from disk
db.collection.find( { "city":"X", location: "A" } ).count()
db.collection.find( { "city":"X", location: "B" } ).count()
db.collection.find( { "city":"X", location: "C" } ).count()
...
BUT, since I do no know all possible elements in advance, what comes to my mind is to use group by, like
db.collection.aggregate([
{ $match: { "city":"X" } },
{ $unwind: "$location" } },
{ $group: { _id: "$location", "amount": { "$sum": 1 } } }
])
However, when explain() this query, only the $match part can utilize the index, after $unwind, fetch data from disk is required (correct me if I am wrong).
Technically, the index contains all information required for the query. So I wonder is there any query that can fully utilize the index.
BTW, my mongo version is 3.6. If it can only be done in newer version, still please let me know. Thanks.