统计MySQL中重叠日期范围的最大数量

CREATE TABLE date_ranges (
  id INT PRIMARY KEY AUTO_INCREMENT,
  start_date DATE,
  end_date DATE
);

INSERT INTO date_ranges (start_date, end_date)
VALUES
  ('2022-01-01', '2022-01-05'),
  ('2022-01-03', '2022-01-07'),
  ('2022-01-06', '2022-01-10'),
  ('2022-01-09', '2022-01-12'),
  ('2022-01-11', '2022-01-15');

SELECT COUNT(*) AS max_overlap
FROM date_ranges dr1
JOIN date_ranges dr2 ON dr1.start_date <= dr2.end_date AND dr1.end_date >= dr2.start_date
WHERE dr1.id <> dr2.id;