PowerShell script to add "Link to a Document" content type to all document libraries

$linkct = "Link to a Document"
$docct = "Document"
Get-SPSite -Limit all | Get-SPWeb -Limit all | ForEach-Object {
    
    $doclibtype =[Microsoft.SharePoint.SPBaseType]::DocumentLibrary
    $doclibs = $_.GetListsOfType($doclibtype)
    
    foreach ($doclib in $doclibs) 
    {
$newdoclib = $_.Lists[$doclib.ID]
    if ($newdoclib.AllowContentTypes)
          {
            $newdoclib.ContentTypesEnabled = $true
           $newdoclib.Update()
    
              #Add site content types to the list
      if (($newdoclib.ContentTypes[$linkct] -eq $null) -and
               ($newdoclib.ContentTypes[$docct] -ne $null))
      {
               $ctToAdd = $_.Site.RootWeb.ContentTypes[$linkct]
               $ct = $newdoclib.ContentTypes.Add($ctToAdd)
               "Content type " + $ct.Name + " added to list " + $newdoclib.Title
               $newdoclib.Update()
            }
         }
     }
}