Have Perl script move a line up in block/group of lines

How can a Perl (preferably one-liner) script move a line up in a block/group of lines in file (# be a comment token):

Code:*****
*FOO=
BAR
BAZ
*FOOBAR
**** # Token such above to start over again repeatedly...
to be:

*****
*FOOBAR
*FOO=
BAR
BAZ
***** # Token such above to start over again repeatedly...Have the script to be simplest/minimal as long as it is working correctly