How to get the previous record date

[sas_student1]

I have a dataset of patients who are admitted and then transferred to another clinic. Sometimes they may get transferred a few times. I would like to get their first admission date and not the transferred date.  For example I have the table with admit_date and dsch_date. You will notice that at times the admit_date repeats for a few records (see client A) but then there is a new record with a new admit_date that is the same as the previous dsch_date. What I would like to do is get the first admit date and last discharge date if it is available. If the dsch_date is missing then the client is still in treatment. I would like to get admit_date1 and dsch_date1 column. 

Client	admit_date	dsch_date	admit_date1	dsch_date1
A	6/28/2002	3/30/2015	6/28/2002	7/12/2019
A	6/28/2002	3/30/2015	6/28/2002	7/12/2019
A	6/28/2002	3/30/2015	6/28/2002	7/12/2019
A	3/30/2015	7/12/2019	6/28/2002	7/12/2019
B	1/9/1998	8/21/2013	1/9/1998	.
B	8/21/2013	.	1/9/1998	.
C	1/29/2008	2/21/2008	1/29/2008	.
C	2/21/2008	2/15/2023	1/29/2008	.
C	2/15/2023	.	1/29/2008	.

Here is the sas code for the table I have:

data have;
input Client:$1. admit_date:mmddyy10. dsch_date:mmddyy10. ;
format admit_date dsch_date mmddyy10.;
datalines;
A 6/28/2002 3/30/2015
A 6/28/2002	3/30/2015
A 6/28/2002	3/30/2015
A 3/30/2015	7/12/2019
B 1/9/1998	8/21/2013
B 8/21/2013	.
C  1/29/2008 2/21/2008
C 2/21/2008	2/15/2023
C 2/15/2023	.

;

run;

Thank you!

[Tom]

Aren't those just the MIN and MAX, respectively, or the two variables you already have?

create table want as 
select *
 ,min(admit_date) as admit_date1 format=mmddyy10. 
 ,max(dsch_date) as dsch_date1 format=mmddyy10. 
from have
group by Client
;