Set-MailboxFolderPermission Default User Question

Hi Guys

Below is a script I've written to set the Default User access rights to None on everyone's Inbox.  My question is, is there a way to start at the root level of a mailbox and set the Default User of every folder to None?

Thanks in advance

Damian

$Mailboxes = Get-Mailbox -ResultSize Unlimited -RecipientTypeDetails UserMailbox | Where-Object {$_.Database -like "Database*"}

ForEach ($Mailbox in $Mailboxes)
{
$Inbox = $Mailbox.PrimarySmtpAddress.ToString() + ":\Inbox"
Set-MailboxFolderPermission -Identity $Inbox -user Default -AccessRights None
}