mongodb count number of distinct values and the sum of each object

Hello i am creating a new Web Application for products selling using MEAN stack and i added some brands(HP,ASUS..) now i created an aggregation to show every brand and how many pc have 8 Gb , how many PC have 4 GB etc. this is my data:

    [
  {
    "_id": ObjectId("617b0dbacda6cbd1a0403f68"),
    "brand": "6178524a5ff14e633aeff1ea",
    "SerialNumber": "45454234324",
    "ram": "4gb"
  },
  {
    "_id": ObjectId("617b0dbacda6cbd1a0403f69"),
    "brand": "6178524a5ff14e633aeff1ea",
    "SerialNumber": "azazz5245454az",
    "ram": "8gb"
  },
  {
    "_id": ObjectId("617b0dbacda6cbd1a0403f70"),
    "brand": "sony",
    "SerialNumber": "azazz5245454az",
    "ram": "8gb"
  },
  {
    "_id": ObjectId("617b0dbacda6cbd1a0403f71"),
    "brand": "sony",
    "SerialNumber": "azazz5245454az",
    "ram": "16gb"
  },
  {
    "_id": ObjectId("617b0dbacda6cbd1a0403f72"),
    "brand": "sony",
    "SerialNumber": "azazz5245454az",
    "ram": "16gb"
  }
]

and this is m code :

    db.b.aggregate([
{$group:{ _id:{ r:"$ram" ,b:"$brand"}, cnt:{$sum:1} }}  ,
{$project:{ a:[{k:"$_id.r" ,v:"$cnt"}] , brand:"$_id.b" ,_id:0}   },
{$project:{d:{$arrayToObject:"$a"} ,brand:1 }  } ,
{$group:{ _id:"$brand", ram:{$push:"$d"}  }} ,
{$project:{_id:0,brand:"$_id" ,"options": { $mergeObjects: "$ram" } }},
{$replaceRoot: {  newRoot: { $mergeObjects: ["$$ROOT", "$options"] }}}, 
{$project:{options:0}}   ])

this what im getting as a result :

{ "brand" : "sony", "16gb" : 2, "8gb" : 1 }

while im trying to get :

{ "brand" : "sony", "16gb" : 2, "8gb" : 1  , "sum" : 3}