module Main where

import Text.Printf (printf)

data ExtInt = NegInfty | Normal Int | PosInfty deriving (Show, Eq, Ord)

adjacentZipper :: (a -> a -> Bool) -> [a] -> ([a], [a])
adjacentZipper cmp items = go [] items
  where go front [] = (front, [])
        go [] (x:rest) = go [x] rest
        go ys@(y:_) xs@(x:rest) = if cmp x y then go (x:ys) rest else (ys, xs)

almostIncreasing :: [Int] -> Bool
almostIncreasing nums = check ([NegInfty] ++ map Normal nums ++ [PosInfty])
  where check items = case adjacentZipper (>) items of
                        (_, []) -> True
                        ((x2:x1:_), right@(y1:y2:_)) -> (x1 < y1 || x2 < y2) && sorted right
        sorted = null . snd . adjacentZipper (>)

main :: IO ()
main = do
  printCase []
  printCase [0, 1]
  printCase [1, 0]
  printCase [5, 1, 2, 3]
  printCase [1, 2, 0, 3]
  printCase [1, 5, 2, 3]
  printCase [1, 5, 0, 2]
  printCase [3, 2, 1, 0]
    where printCase xs = printf "%s => %s\n" (show xs) (show $ almostIncreasing xs)