MongoDB query remove bottom 10% extreme values for each specific type of data - mongodb

Question

Let's say I have a MongoDB storing transaction prices of a few products like this:
[
{
"_id": 1,
"product": "A",
"price": NumberDecimal("1.00")
},
{
"_id": 2,
"product": "A",
"price": NumberDecimal("20.00")
},
{
"_id": 3,
"product": "A",
"price": NumberDecimal("30.00")
},
{
"_id": 4,
"product": "B",
"price": NumberDecimal("10.00")
},
{
"_id": 5,
"product": "B",
"price": NumberDecimal("200.00")
},
{
"_id": 6,
"product": "B",
"price": NumberDecimal("300.00")
}
]
I want to remove bottom 10% of the extreme transaction prices, I do this:
db.collection.aggregate([
{
$bucketAuto: {
groupBy: "$price",
buckets: 10,
output: {
docs: {
$push: "$$ROOT"
}
}
}
},
{
$skip: 1
},
{
$unwind: "$docs"
},
{
$replaceWith: "$docs"
}
])
The outcome is like this:
[
{
"_id": 4,
"price": NumberDecimal("10.00"),
"product": "B"
},
{
"_id": 2,
"price": NumberDecimal("20.00"),
"product": "A"
},
{
"_id": 3,
"price": NumberDecimal("30.00"),
"product": "A"
},
{
"_id": 5,
"price": NumberDecimal("200.00"),
"product": "B"
},
{
"_id": 6,
"price": NumberDecimal("300.00"),
"product": "B"
}
]
The extreme transaction price 1.00 is removed. But I actually want the extreme 10% prices for each product to be removed, so that price 1.00 of product A is removed, and price 10.00 for product B is also removed. Expected result should be:
[
{
"_id": 2,
"price": NumberDecimal("20.00"),
"product": "A"
},
{
"_id": 3,
"price": NumberDecimal("30.00"),
"product": "A"
},
{
"_id": 5,
"price": NumberDecimal("200.00"),
"product": "B"
},
{
"_id": 6,
"price": NumberDecimal("300.00"),
"product": "B"
}
]
How can I achieve this? I have something very close but it is hard coding the product names in the query, which is very wrong:
https://mongoplayground.net/p/ur3Qmr2VJKb