Sorting groups of lines

Question

Say I have this list:

sharpest
  tool
  in
the
  shed
im
  not
  the

How can I order alphabetically by the non-indented lines and preserve groups of lines? The above should become:

im
  not
  the
sharpest
  tool
  in
the
  shed

Similar questions exist here and here but I can't seem to make them work for my example.

Hopeful ideas so far

• Maybe I could use grep -n somehow, as it gives me the line numbers? I was thinking to first get the line numbers, then order. I guess I'd somehow need to calculate a line range before ordering, and then from there fetch the range of lines somehow. Can't even think how to do this however!
• sed ranges look promising too, but same deal; sed 1,2p and further examples here.

Answer 1

If perl is okay:

$ perl -0777 -ne 'print sort split /\n\K(?=\S)/' ip.txt
im
  not
  the
sharpest
  tool
  in
the
  shed

• -0777 slurp entire file, so solution not suitable if input is too big
• split /\n\K(?=\S)/ gives array using newline character followed by non-whitespace character as split indication
• sort to sort the array