Pass data from Sunday to week before in MongoDB - mongodb

Question

My aggregation gets the data of documents per week. In this case I'm getting data from days 18 to 24 of may:
{ "_id" : 20, "count" : 795 }
{ "_id" : 21, "count" : 221 }
Since 'week' in mongo starts from sundays, the data from sundays is creating a new week (In this case is 21). Is there any way I can transfer the data from Sundays to the week before or backwards?
The result would be:
{ "_id" : 20, "count" : 1016 }
Aggregation:
[{
$match: {
start_date: {
$gte: ISODate('2020-05-18T00:00:01'),
$lte: ISODate('2020-05-24T23:59:59')
}
}
}, {
$project: {
week: {
$week: '$start_date'
},
solved: '$solved',
survey: '$survey'
}
}, {
$group: {
_id: '$week',
count: {
$sum: 1
}
}
}, {
$sort: {
_id: 1
}
}]
UPDATE:

Answer 1

I think the below query will do the trick.
The timezone key in if condition can be removed if your week-wise-sort is independent of the time zone of ISODate value in DB
db.<Collection-Name>.aggregate([
{
$match: {
start_date: {
$gte: ISODate('2020-05-18T00:00:01'),
$lte: ISODate('2020-05-24T23:59:59')
}
}
}, {
$project: {
week: {
"$cond": {
"if": {"$eq": [{"$dayOfWeek": {"date": "$start_date", "timezone": "-0500"}}, 1]},
"then": {"$subtract": [{"$week": '$start_date'}, 1]},
"else": {"$week": '$start_date'}
}
},
solved: '$solved',
survey: '$survey'
}
}, {
$group: {
_id: '$week',
count: {
$sum: 1
}
}
}, {
$sort: {
_id: 1
}
}
])