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You are given user signup data and product activity data for a self-serve AI product. Write a PostgreSQL query that builds monthly signup cohorts and measures retention by month offset. A user belongs to the cohort of their signup month, and they are retained in month n if they had at least one qualifying activity in the nth calendar month after signup. Return one row per cohort month and month offset for offsets 0, 1, and 2, including cohort size, retained users, and retention rate.
