Challenge #367 [Easy] Subfactorials - Another Twist on Facto

    function Derangement
    {
        param (
            [bigint]$n
        )

        process
        {

            switch ($n)
            {
                ({ $global:cache.ContainsKey($n) }) { $r = $global:cache[$n]; break }
                0 { $r = 1; break }
                1 { $r = 0; break }
                default
                {
                    $r = ($n - 1) * ((Derangement($n - 1)) + (Derangement($n - 2)))
                    $global:cache[$n] = $r
                }
            }
            Write-Output $r

        }

    }


    $cache = @{ }

    $ChallengeInput = @(6, 9, 14) | ForEach {

        Write-Host "The Derangement of $_ is $(Derangement $_)"

    }