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Mongoose | Find objects inside of an array, that each object has another array of objects to satisfy condition

I have a collection Shops . Each object in Shops collection has an array of Item objects called items .

{
    _id: ObjectId(...),
    shopName: 'Ice cream Shop',
    items: [ 
        <Item>{
            itemName: 'Chocolate IC',
            availabilities: [
                {
                    city: 'NY',
                    arrivals: [
                        {
                            price: 3.99,
                            quantityLeft: 0,
                            date: 'yesterday'
                        },
                        {
                            price: 3.99,
                            quantityLeft: 40,
                            date: 'today'
                        }
                    ]
                },
                {
                    city: 'LA',
                    arrivals: []
                }
            ]
        },
        <Item>{
            itemName: 'Strawberry IC',
            availabilities: [
                {
                    city: 'NY',
                    arrivals: [
                        {
                            price: 3.99,
                            quantityLeft: 0,
                            date: 'yesterday'
                        },
                    ]
                }
            ]
        },
    ],
},
... anotherShops

I want to get list of Item objects which has overall quantityLeft more than 0 from a specific shop . I tried this code to get all items with the name start with "Straw" from a Shop with shopName equal to 'Ice cream Shop' :

const items = await Shop.aggregate()
    .match({
        shopName: 'Ice cream Shop',
    })
    .project({
        items: {
            $filter: {
                input: "$items",
                as: "item",
                cond: {
                    $regexMatch: {
                        input: "$$item.itemName",
                        regex: `.*Straw.*`,
                    },
                },
            },
        },
    });

And it works. But I don't know how to sum up all quantityLeft values inside availabilities array of each item , and return only that items that has sum more than 0.

availabilities array can be an empty array [].

The city parameter also needs to be in condition. For example, only Items that are in stock in NY

I need this to get the list of items from a certain shop, and only the items that are still in stock. Pretty hard.

I came up with this solution. If you have a better solution, please post it.

const shop = await GCShop.aggregate([
    {
        $match: {
            shopName: 'Ice Cream Shop',
        },
    },
    {
        $unwind: "$items",
    },
    {
        $unwind: "$items.availabilities",
    },
    {
        $unwind: "$items.availabilities.arrivals",
    },
    {
        $group: {
            _id: "$items.id",
            items_name: { $first: "$items.name" },
            arrivals: {
                $push: {
                    arrival_id: "$items.availabilities.arrivals.arrival_id",
                    price: "$items.availabilities.arrivals.price",
                    qtty: "$items.availabilities.arrivals.qtty",
                },
            },
            totalQtty: { $sum: "$items.availabilities.arrivals.qtty" },
        },
    },
    {
        $project: {
            offer_id: "$_id",
            _id: 0,
            offer_name: 1,
            totalQtty: 1,
            arrivals: 1,
        },
    },
    {
        $match: {
            totalQtty: {
                $gt: 0,
            },
        },
    },
]).limit(20);

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