How to update colum serial where is null by max+1 ?

Question

I work on SQL server 2012 I face issue i can't update column serial by max + 1
where is have null value on on serial column
partnumber is unique on table
so i need to get max number from serial and increment it by 1
then assign it to null on serial column

meaning any partnumber is unique and have null on serial
must have unique number on serial by max number on serial +1

for every part number

 create table #test
 (
 partNumber  nvarchar(200),
 serialNumber  int
 )
 insert into #test(partNumber,serialNumber)
 values
 ('nna5',9),
 ('nfggg',20),
 ('ddfg',10),
 ('llm',NULL),
 ('109',NULL),
 ('8654',NULL),
 ('1234',30)

expected result

partNumber serialNumber
llm 31
109 32
8654 33