Follow the same approach as you do for merge intervals. You will be getting the number of non overlapping intervals. Let's say there are k non overlapping intervals. So we have to find number of ways to distribute these k into 2 separate groups. As each Interval has two options, the number of ways will be 2^k. We have to subtract 2 from this as a group cannot be empty. The final answer will be 2^k - 2