SQL: Churn Rate by Cohort Month

NewWave Telecom & Technologies wants to monitor customer retention in its NewWave Connect service. Write a PostgreSQL query that calculates monthly churn by customer cohort, where a cohort is defined by the month of a customer's first non-null usage event.

A customer is considered active in a month if at least one usage event exists. Churn occurs when a customer was active in the previous month but is inactive in the current month. The analysis should continue through the latest usage month in the data.

Requirements

1. Return cohort_month, month_number, cohort_size, active_customers, churned_customers, and churn_rate.
2. Use the previous month's active customer count as the churn-rate denominator.
3. Return a zero churn rate for the cohort's starting month and months with no previous active customers.
4. Include months with no active customers, and order the result by cohort month and month number.