Using test-path to check for file existence in four network directories

I'm trying to test for the existence of a file in 4 unc paths.  Using test-path I know how to check for the existence in one unc path as such:

test-path \\networkshare\folder\file.txt

How would I go about building this out to check for the file in 4 other network paths.  I've tried to create an array to store the the network paths such as:

$directories = "\\networkshare1\folder", "\\networkshare2\folder", "\\networkshare3\folder", "\\networkshare3\folder"

and assigned the file name to a variable as such:

$filename = file.txt

After that, I tried to pipeline in the filename to the $directories varialbe as such:

$directories | test-path $filename

This is not working.