How to make perl match a run of spaces and newlines?

test.sh

# File "bar"'s whitespace consists only of spaces and newlines.
$ cat bar
1, 2,
  3,
4

# All attempts to replace consecutive runs of whitespace (spaces and newlines) with 'S' 
# result in \n being replaced by one 'S', and spaces that follow it replaced by another 'S'.
# Desired output: 1,S2,S3,S4S
# Actual output:  1,S2,SS3,S4S
$ cat bar | perl -pe 's/\s+/S/g'
1,S2,SS3,S4S
$ cat bar | perl -pe 's/\s+/S/gm'
1,S2,SS3,S4S
$ cat bar | perl -pe 's/\s+/S/gms'
1,S2,SS3,S4S
$ cat bar | perl -pe 's/[ \n]+/S/gms'
1,S2,SS3,S4S
$ cat bar | perl -pe 's/[ \n]+/S/gm'
1,S2,SS3,S4S
$ cat bar | perl -pe 's/[ \n]+/S/g'
1,S2,SS3,S4S