mongodb update value in 3 level nested array of objects - node.js

Question

I want to update flag in array of objects which are 3 levels deep nested.
I have this array of ages:
[20, 25]
I want to set flag: 1 for those users which has type: students and ages: 20 or 25
Here is my Users collection:
{
"_id": "wef324DGSshf",
"userTypes": [
{
"type": "students",
"users": [
{
"name": "John",
"age": 20,
"flag": 0
},
{
"name": "Mike",
"age": 25,
"flag": 0
}
]
},
{
"type": "students",
"users": [
{
"name": "Henry",
"age": 40,
"flag": 0
},
{
"name": "Nick",
"age": 25,
"flag": 0
}
]
},
{
"type": "teachers",
"users": [
{
"name": "Kim",
"age": 20,
"flag": 0
},
{
"name": "Charles",
"age": 25,
"flag": 0
}
]
}
]
}
After update I expect this response:
{
"_id": "wef324DGSshf",
"userTypes": [
{
"type": "students",
"users": [
{
"name": "John",
"age": 20,
"flag": 1
},
{
"name": "Mike",
"age": 25,
"flag": 1
}
]
},
{
"type": "students",
"users": [
{
"name": "Henry",
"age": 40,
"flag": 0
},
{
"name": "Nick",
"age": 25,
"flag": 1
}
]
},
{
"type": "teachers",
"users": [
{
"name": "Kim",
"age": 20,
"flag": 0
},
{
"name": "Charles",
"age": 25,
"flag": 0
}
]
}
]
}
What I have tried so far is this query:
Users.update(
{ "userTypes.users.age": { $in: [20,25] } },
{ "$set": { "userTypes.users.$.flag": "1" } }
);
My solution is not updating the desired records, can anyone help me with the right query for this case?