Replacing "Everyone" with "Authenticated Users" for Print$ with PowerShell

Good Evening all.  I am currently trying to figure out how to either 1) replace the existing Everyone group on the Print$ share with Authenticated Users or 2) use PowerShell to add Authenticated Users with Read access to print$ share.  I have used some resources available on the net and I am able to now remove the Everyone group from the Share, but I have been unable to find a way to add Authenticated Users.  Any help would be greatly appreciated.  here is the code I am using currently.

###################################################################################
#                                                                                 #
# Script to remove Everyone from a share and replace it with Authenticated Users. #
#                                                                                 #
###################################################################################
function GetSecurityDescriptor($ShareName)
{
    $LSSS = Get-WmiObject -Class "Win32_LogicalShareSecuritySetting" -computername $computer | where {$_.Name -eq $shareName}
    $Result = $LSSS.GetSecurityDescriptor()
    if($Result.ReturnValue -ne 0)
    {
        throw "GetSecurityDescriptor Failed"
    }
    # if return value is 0, then we can get its security descriptor 
    $SecDescriptor = $Result.Descriptor
    return $SecDescriptor
}
 
function SetShareInfo($ShareName,$SecDescriptor)
{
    $Share = Get-WmiObject -Class "Win32_Share" -computername $Computer | where {$_.Name -eq $shareName}
    $MaximumAllowed = [System.UInt32]::MaxValue
    $Description = "After remove permission"
    $Access = $SecDescriptor
    $Result = $Share.SetShareInfo($MaximumAllowed,$Description,$Access)
    if($Result.ReturnValue -ne 0)
    {
        throw "SetShareInfo Failed"
    }
    "Success!"
}
 
function GetIndexOf($DACLs,$Domain,$Username)
{
    $Index = -1;
    for($i = 0; $i -le ($DACLs.Count - 1); $i += 1)
    {
        $Trustee = $DACLs[$i].Trustee
        $CurrentDomain = $Trustee.Domain
        $CurrentUsername = $Trustee.Name
       
        
        if($CurrentUsername -eq $Username)
        {
            $Index = $i
        }
    }
    return $Index
}
 
function RemoveDACL($DACLs,$Index)
{
    if($Index -eq 0)
    {
        $RequiredDACLs = $DACLs[1..($DACLs.Count-1)]
    }
    elseif ($Index -eq ($DACLs.Count-1))
    {
        $RequiredDACLs = $DACLs[0..($DACLs.Count-2)]
    }
    else
    {
        $RequiredDACLs = $DACLs[0..($Index-1) + ($Index+1)..($DACLs.Count-1)]
    }
    return $RequiredDACLs
}
 
function RemoveSharePermissionOf($Domain,$Username,$ShareName)
{
    $SecDescriptor = GetSecurityDescriptor $ShareName
    # get DACL
    $DACLs = $SecDescriptor.DACL
    # no DACL
    if($DACLs -eq $null)
    {
        "$ShareName doesn't have DACL"
        return
    }
    # find the specific DACL index
    $Index = GetIndexOf $DACLs $Domain $Username
    # not found
    if($Index -eq -1)
    {
        "User $Domain\$Username Not Found on Share $ShareName"
        return
    }
    # remove specific DACL
    if(($DACLs.Count -eq 1) -and ($Index -eq 0))
    {
        $RequiredDACLs = $null
    }
    else
    {
        $RequiredDACLs = RemoveDACL $DACLs $Index
    }
    # set DACL
    $SecDescriptor.DACL = $RequiredDACLs
    
    SetShareInfo $ShareName $SecDescriptor
}
$Domain=""
$Username="Everyone"
$ShareName="Print$"
$ComputerList = Get-Content c:\Print-input.txt
    ForEach ($Computer in $ComputerList)
    {
        RemoveSharePermissionOf $Domain $Username $ShareName
    }

Thank you all.

Kevin