What can I use to get the paths of all parent directories for a given path

I'm looking for a tool that I can use from a bash script that can give me the list of parent directories for a given path. e.g. given the input foo/bar/moocow I would like to get out:

foo
foo/bar
foo/bar/moocow

It would also be great if I could pipe in multiple paths, and get unique results back, e.g.:

toolimlookingfor << EOF
dir1/file1
dir1/file2
foo/bar/moocow
EOF

Output:

dir1
dir1/file1
dir1/file2
foo
foo/bar
foo/bar/moocow

dirname is close to what I'm looking for, but it only gives the immediate parent. I'm looking for the path it's self and all parents.