mongodb iterate over array elements without unwind

Question

[
  {
    "_id": 1,
    c: [
      {
        d: [
          {
            b: [
              {
                a: 1
              },
              {
                a: 2
              },
              {
                a: 2
              },
              {
                a: 2
              }
            ]
          }
        ]
      }
    ]
  }
]

We have this sample data and the question is // count() how many are the "c.d.b.a":2 in the collection // Final result: {"a":3} We can do it with unwind but the data is very big and unwind operation performance not good for big collections. Is there any other solution to this problem. playground

I have tried it with unwind but finding another solution without unwind operator