SQL Time Between Visits

Tempus Lens uses longitudinal patient records to support clinical insights. Given a patient visit table, write a PostgreSQL query that measures the interval between each patient's first and second completed visits.

Requirements

1. Consider only visits with visit_status = 'completed' and a non-null visit_started_at.
2. Number each patient's valid visits chronologically, using visit_id to break timestamp ties.
3. Return only patients with at least two valid completed visits, including the first visit timestamp, second visit timestamp, and elapsed interval.
4. Sort the final results by patient_id.