mongodb aggregation multiple unknown nested keys

I have a document called 'InventoryPerDay' that contain inventory for stores for each day:

{
  _id: "20131202/store_a",
  _metadata: {
    date: ISODate("2013-12-02T00:00:00Z"),
    store: "store_a"
  },
  inventory: {
    quantity: {
      item_44: 1350,
      item_32: 1,
      item_2: 1,
      item_9: 1
    }
  }
},
{
  _id: "20131201/store_a",
  _metadata: {
    date: ISODate("2013-12-01T00:00:00Z"),
    store: "store_a"
  },
  inventory: {
    quantity: {
      item_44: 1000,
      item_32: 5,
      item_2: 10
    }
  }
}

I need the total quantity of each item in store_a for both of the days. The items in the 'quantity' hash are unknown. You can see that 'item_9' exists for 02/12/2013 but not for 01/12/2013.

How can i sum unknown nested keys in multiple documents using aggregation in mongodb?

The result for the above example should be:

{
  store: "store_a",
  inventory: {
    quantity: {
      item_44: 2350,
      item_32: 6,
      item_2: 11,
      item_9: 1
    }
  }
}