MongoDB Aggregation for building conditional sums

Let's pretend I have some user documents in my MongoDB. Every user has a type (int) and presence days (boolean).

my documents schema

{
  type: NumberInt() // 1|2|3
  presence: {
    day1: true,
    day2: false,
    day3: true
}

I want to count the precence days for each type of user to visualize their precence in a line chart. The needed output has to look like this. Three objects in an array representing the types. Every object has series. They represent the sum of users of a specific type present at the named day.

wanted result

[{
  name: "Type1"
  series: [{
    name: "Day1",
    value: 5, // count (type==1 && d1==true)
  }, {
    name: "Day2",
    value: 8, // count (type==1 && d2==true)
  }, {
    name: "Day3",
    ...
  }]
}, {
  name: "Type2"
  series: [{
    name: "Day1",
    value: 10, // count (type==2 && d1==true)
  }, {}, {}]
}, {
  name: "Type3"
  series: [{}, {}, {}]
}, {
  name: "AllCombined"
  series: [{}, {}, {}]
}]

Question

How can I achive that with mongodb aggregation? I played around with $match, $sort, $project, $sum but I couldn't figure it out. Thanks in advance

requested samples: user collection

{_id: ..., type: 1, presence: {d1:true, d2: true, d3: false}}
{_id: ..., type: 2, presence: {d1:false, d2: true, d3: false}}
{_id: ..., type: 3, presence: {d1:true, d2: false, d3: true}}
{_id: ..., type: 1, presence: {d1:true, d2: false, d3: false}}

You can use below aggregation

db.collection.aggregate([
  { "$group": {
    "_id": "$type",
    "d1": { "$sum": { "$cond": [{ "$eq": ["$presence.d1", true] }, 1, 0] }},
    "d2": { "$sum": { "$cond": [{ "$eq": ["$presence.d2", true] }, 1, 0] }},
    "d3": { "$sum": { "$cond": [{ "$eq": ["$presence.d3", true] }, 1, 0] }}
  }},
  { "$project": {
    "_id": 0,
    "name": { "$concat": ["Type", { "$toString": "$_id" }] },
    "series": [
      {
        "name": "Day1",
        "value": "$d1"
      },
      {
        "name": "Day2",
        "value": "$d2"
      },
      {
        "name": "Day3",
        "value": "$d3"
      }
    ]
  }}
])