module _92

open common

let squareChainLoop =
    
    let squareDigits d =
        let square n = n * n
        d |> numDigits |> Seq.map square |> Seq.sum

    let chainDict = new System.Collections.Generic.Dictionary<int,int>()
    let rec chainCache = function
        | x when chainDict.ContainsKey(x) -> chainDict.[x]
        | 1 -> 1
        | 89 -> 89
        | x -> chainDict.[x] <- chainCache (squareDigits x); chainDict.[x]
            
    allIntegers |> Seq.skip 1 |> Seq.takeWhile ((>) 10000000)
    |> Seq.map chainCache
    |> Seq.filter ((=) 89)
    |> Seq.length