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Optimize: Advent of Code Day 6 w/: toggling lights in a grid with Powershell

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I am using the "Advent of Code" series to help with my Powershell education. http://adventofcode.com/day/6

I am confident that this script will produce the right answer. However, it is going way to slow. I am interested in optimizing this script for improved performance. I am not against coming up with an alternative way to solve this problem with powershell.

$lightson = New-Object Collections.Generic.HashSet[string]
$strings = Get-Content C:\test\lights.txt
foreach ($string in $strings){
 $numbers = [regex]::matches($string,"\d+")
 $minX = [convert]::ToInt32($numbers[0],10)
 $minY = [convert]::ToInt32($numbers[1],10)
 $maxX = [convert]::ToInt32($numbers[2],10)
 $maxY = [convert]::ToInt32($numbers[3],10)
 $x = $minX
 $y = $miny
 write-host $string
 write-host $x $y
 if ($string -like "turn on*"){
 write-host "turn on"
 while ($x -le $maxX){
 while ($y -le $maxY){
 $light = "$x,$y"
 if ($light -notin $lightson){
 [void]$lightson.Add("$x,$y")
 #write-host $lightson.Count
 }
 $y +=1
 }
 $x += 1
 $y = $miny
 }
 write-host $lightson.Count "`n"
 }
 if ($string -like "turn off*"){
 write-host "turn off"
 while ($x -le $maxX){
 while ($y -le $maxY){
 $light = "$x,$y"
 if ($light -in $lightson){
 [void]$lightson.Remove("$x,$y")
 #write-host $lightson.Count
 }
 $y +=1
 }
 $x += 1
 $y = $miny
 }
 write-host $lightson.Count "`n"
 }
 if ($string -like "toggle*"){
 write-host "toggle`n"
 while ($x -le $maxX){
 while ($y -le $maxY){
 $light = "$x,$y"
 if ($light -in $lightson){
 $lightson.Remove("$x,$y")
 #write-host $lightson.Count
 }
 else{[void]($lightson.Add("$x,$y"))}
 $y +=1
 }
 $x += 1
 $y = $miny
 }
 write-host $lightson.Count "`n"
 }
}

There are a million different lights that can be on or off. This massive number is obviously causing the long process time. At the moment, I can not think of any alternatives.

Thank you in advance