PostgreSQL: running count of rows for a query 'by minute'

I need to query for each minute the total count of rows up to that minute.

The best I could achieve so far doesn't do the trick. It returns count per minute, not the total count up to each minute:

SELECT COUNT(id) AS count
, EXTRACT(hour from "when") AS hour
, EXTRACT(minute from "when") AS minute
FROM mytable
GROUP BY hour, minute

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