Problem:
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Maximum Profit

You can obtain profits from foreign exchange margin transactions. For example, if you buy 1000 dollar at a rate of 100 yen per dollar, and sell them at a rate of 108 yen per dollar, you can obtain (108 - 100) × 1000 = 8000 yen.

Write a program which reads values of a currency $R_t$ at a certain time $t$ ($t = 0, 1, 2, ... n-1$), and reports the maximum value of $R_j - R_i$ where $j > i$ .

Input

The first line contains an integer $n$. In the following $n$ lines, $R_t$ ($t = 0, 1, 2, ... n-1$) are given in order.

Output

Print the maximum value in a line.

Constraints

$2 \leq n \leq 200,000$

$1 \leq R_t \leq 10^9$

Sample Input 1

6
5
3
1
3
4
3

Sample Output 1

3

Sample Input 2

3
4
3
2

Sample Output 2

-1

Solution in Haskell (judge verdict: Memory Limit Exceeded)

import Data.List

max' Nothing  Nothing  = Nothing
max' (Just a) Nothing  = Just a
max' Nothing  (Just b) = Just b
max' (Just a) (Just b) = Just $ max a b

  -- max: ?????????????????§???, s:?°??????????????????????list, r:??§?????????????????????list
search :: Int -> [(Int,Int)] -> [(Int,Int)] -> Maybe Int
search _ _ [] = Nothing
search _ [] _ = Nothing
search cur_max s r =
  let (ln,lv) = head s
      (hn,hv) = head r
      val     = hv - lv
  in
    if val < cur_max
    then Nothing -- finish
    else
      let new_max = if ln < hn
                    then max cur_max val
                    else cur_max
          s1 = tail s
          r1 = tail r
          x0 = search new_max s r1
          x1 = search new_max s1 r
      in 
        if ln < hn
        then max' (Just val) $ max' x0 x1
        else max' x0 x1
ans x = 
    let (x0:x1:_) = x
        init_max  = x1 - x0
        s = sortBy (\(na,va) (nb,vb) -> compare va vb) $ zip [1..] x
        r = reverse s
        v = max' (Just init_max) (search init_max s r)
    in
      v

main = do
    n <- getLine
    c <- getContents
    let i = map read $ lines c :: [Int]
        (Just o) = ans i
    print o