Python django-获取日期范围重叠的所有模型实例

假设我有以下模型：

class DateRange(models.Model):
    start = models.DateTimeField()
    end = models.DateTimeField()

是否有一种方法可以获取所有在

start

到

end

范围内有重叠的日期范围实例对？例如，如果我有：

  id |  start              |  end
-----+---------------------+---------------------
   1 | 2020-01-02 12:00:00 | 2020-01-02 16:00:00  # overlap with 2, 3 and 5
   2 | 2020-01-02 13:00:00 | 2020-01-02 14:00:00  # overlap with 1 and 3
   3 | 2020-01-02 13:30:00 | 2020-01-02 17:00:00  # overlap with 1 and 2
   4 | 2020-01-02 10:00:00 | 2020-01-02 10:30:00  # no overlap
   5 | 2020-01-02 12:00:00 | 2020-01-02 12:30:00  # overlap with 1

我想要：

 id_1 | id_2
------+-----
    1 |    2
    1 |    3
    1 |    5
    2 |    3

你有没有想过最好的方法？id_1和id_2的顺序并不重要，但我确实需要区分（例如-

id_1=1，id_2=2

与

id_1=2，id_2=1

相同，不应重复）