import Data.Array (Array, array, listArray, (!))

maxDoubleSliceSum :: [Int] -> Int
maxDoubleSliceSum a
  | n < 3     = 0
  | otherwise = maximum [p1 ! i + p2 ! i | i <- [1 .. n - 2]]
  where
    n   = length a
    arr = listArray (0, n - 1) a :: Array Int Int

    -- p1 ! i = best sum of a slice ending just before index i, growing left to right
    p1list = scanl (\acc i -> max 0 (acc + arr ! (i - 1))) 0 [2 .. n - 2]
    p1     = listArray (1, n - 2) p1list :: Array Int Int

    -- p2 ! i = best sum of a slice starting just after index i, growing right to left
    p2list = scanl (\acc k -> max 0 (acc + arr ! (k + 1))) 0 [n - 3, n - 4 .. 1]
    p2     = array (1, n - 2) (zip [n - 2, n - 3 .. 1] p2list) :: Array Int Int