Count of records between min date range and other date

I'm trying to get the count of records of users who appear between a certain date range, specifically the min(date) for each unique user and that min(date) + 14 days. I've checked this link SQL HAVING BETWEEN a date range but it's not what I'm looking for. Here's an example of what I'm working with and what I've tried to do

+----+------------+
| ID | ServiceDt  |
+----+------------+
| 10 | 2017-03-02 |
| 10 | 2017-03-05 |
| 10 | 2017-03-06 |
| 10 | 2017-03-14 |
| 10 | 2017-03-27 |
| 11 | 2017-03-10 |
| 11 | 2017-03-19 |
| 11 | 2017-04-02 |
| 11 | 2017-04-14 |
| 11 | 2017-04-23 |
| .. | ..         |

The query is:

SELECT ID, COUNT(ServiceDt) AS date_count 
FROM (
     SELECT ID, ServiceDt
     FROM tbl 
     GROUP BY ID, ServiceDt
     HAVING ServiceDt BETWEEN MIN(ServiceDt) AND DATEADD(day, +14, MIN(ServiceDt))
) AS R1
GROUP BY ID

When I do the above query I get the following result.

+----+------------+
| ID | date_count |
+----+------------+
| 10 | 5          |
| 11 | 5          |
| .. | ..         |

I also tried using CONVERT(date, ...), but I get the same resulting table above. I want the result to be

+----+------------+
| ID | date_count |
+----+------------+
| 10 | 4          |
| 11 | 2          |
| .. | ..         |

Can someone please guide me on what I can do to get my desired output, thanks

Copyright Notice：Content Author:「Nicholas」，Reproduced under the CC 4.0 BY-SA copyright license with a link to the original source and this disclaimer.
Link to original article：https://stackoverflow.com/questions/43947603/count-of-records-between-min-date-range-and-other-date