A challenge for MySQL experts

Good afternoon, I came across a problem that was simple in appearance, but to solve which you need to move your brains well :)

So: we have the following table:

id	rating	place
1	86	Null
2	5	Null
3	5	Null
4	41	Null
5	1	Null
6	91	Null

It is necessary to put down a place in the rating of each record, based on points (rating), and if the points coincide, use a secondary attribute (in this case, id). As a result, you need to get the following table:

id	rating	place
1	86	5
2	5	2
3	5	3
4	41	4
5	1	1
6	91	6

Important note: the answer must be a single UPDATE query (you can use nested SELECT queries).

Waiting for suggestions :)