-------------------------------------------------------------------------------- 
    -- Tue Nov 20 21:24:09 2018 
    -- Get maximum value in constant time 
    -- push() and pop(), getMax(), top(), isEmpty()
    -------------------------------------------------------------------------------- 
    newtype Stack a   = Stk a deriving (Show)

    empty_            = Stk []
    push_ x (Stk xs)  = Stk (x:xs)
    pop_ (Stk (x:xs)) = Stk xs
    top_ (Stk (x:xs)) = x
    isEmpty_ (Stk xs) = null xs
    get (Stk xs)      = xs

    getMax::Stack [Int] -> Int 
    getMax (Stk []) = 0 
    getMax (Stk (x:cx))  = x 

    xpush::Int->Stack [Int]->Stack [Int]->(Stack [Int], Stack [Int])
    xpush n (Stk xs) (Stk ys) = if isEmpty_ (Stk ys) || (top_ (Stk ys)) < n 
                                then (push_ n (Stk xs), push_ n (Stk ys)) 
                                else (push_ n (Stk xs), Stk ys)

    xpop::Stack[Int]->Stack[Int]->(Stack[Int], Stack[Int])
    xpop (Stk (x:cx)) (Stk (y:cy)) = if x == y 
                                     then ((Stk cx), (Stk cy)) 
                                     else ((Stk cx), (Stk (y:cy)))