Powershell set length of empty array

Question

I want to fill the array with gussed correct letters from the solution $Solution but everytime comes the error

"Index was outside the bounds of the array"

($arrayOutput).length=$LengthSolution doesnt work

$Solution="Apfelpfannekuchen"

$arraySolution = $Solution.ToCharArray()

$LengthSolution=($Solution|measure-object -Character).Characters

$arrayOutput@()a

while ($Input -notmatch $ Solution) {

[string]$Input = Read-Host "choose a letter"

    $arrayInput = $ Input.ToCharArray()

 

    for ($i = 0; $i -lt $LengthSolution; $i++) {

        if($Input -eq $arraySolution[$i]){$arrayOutput[$i]=$Input}

        else {}

    }

    $arrayOutput

}